This is going to be long but:
LITERALLY ALL OF THIS !! One of vld's main issues is how they establish something and never elaborate on it further. It's like boom this story is this, and we all get the gist of it, could be cool to really delve deep into it, but for some reason they never do? Idk if it was a production problem or if the writers kept changing or forgetting shit.
Shiro being the crew's older brother figure and leader could've been fleshed out in a non-action episode. They could've strengthened the paladin's bond with and showed us smth outside of him being this prodigy fighter and someone ppl look up. Shiro has some insane humor like his comments if you pay attention feel so crazy ARE YOU OKAY??? He's been through so much but outside of Keith, nobody really knows this dude and a fun episode could've fixed it idk. They had the opportunity with Pidge and her connection to the Kerberos mission, Lance who looked up to him, Allura who also is in the same position of being a leader, and Hunk who's a guy who is afraid of a lot of things compared to Shiro who's the decision maker who's really not allowed to. Like a bonding episode could've been nice. With all of them. (maybe acknowledging Shiro's trauma butttt let's not get ahead of ourselves.)
and like OP said an episode where Shiro, Lance, and Keith teaching them how to fly could've been so cute to see, maybe show us where their passion comes from and highlight the team's differences. This could, in turn, show us them trying to figure out a flow that works for them since they did just JUMP into this saving universe shit without any prep.
We could've had more focus on the Blades and who they are and their cultures as a fun episode, bc when Keith dipped, brother fucking DIPPED. Nobody's saying anything about him (to be fair they are busy) but we should've been able to see his side with the blades and had a fun episode with them that humanized their side. And this could've made Keith reuniting with his mom hit a LOT harder. After all, what's the point of hyping up his mother and adding mystery to it if she's from an organization they've barely focused on or care to explore more. We could've seen their cultural differences, he could've learned some of the language, could've compared this to his home life back on earth bc his mother is alive, she is out here, and he was in what I assume is fucking foster care constantly being dragged by some shady adults all his life for his behavioral issues. (See he's stronger than me, if I was him, I'd be pissed off).
Pidge's whole thing with her family. Genuinely think her story is the only one where they did it some sort of justice. But even then, her and Shiro not having more interactions is so upsetting. What do you mean, she barely interacts with the person who knew what happened to her family? No late-night talks, no Shiro teaching Pidge something that reminds her of her brother, No Pidge asking what Matt was like in school c'mon. We could've made history. There's also Pidge and Keith having a connection to Shiro, but also being the only two to constantly be known to act out of line due to something personal happening to them. Ppl might view them as brats, and they were lowkey at each other's throats in s1 bc Katie had someone to back home to, She has a family to find, meanwhile Keith cannot relate. They literally could've expanded on that. Gave them a bonding scene or episode. Pidge and Hunk are seen together quite a lot in the show but they should've bonded more. Outside of being tech-brainiacs, there's the whole family thing. Hunk has a family- a big one at that, waiting for him back at home. He loves them so much and misses them constantly but it was only ever brought up in s7. They should've expanded and introduced that WAYYY back in s1 when Pidge was looking for her family. She wanted to leave, she has a family to look for, but Hunk he's tired of constantly being dragged into shit. He hasn't been able to breathe, and this whole space paladin thing is new to him, to everyone, but it only seems like he's the one truly reacting to how crazy everything is. Like wdym WE ARE IN SPACE?? The other day we were at the Garrison studying for an exam, eating edible food, and now we're talking to fucking aliens. HOW?? HELLO??? Lance, instead of being viewed as the dumb one, could've made their differences work hand in hand. Pidge has her tech stuff, she's the one analyzing the data to track the empire's shit, and Lance, he's all about the action coordinating their attack times, the sharpshooter, being acknowledged as a good pilot bc for some reason they never do? which causes them to talk about his insecurities (and also not everyone can be a pilot, you kinda have to be smart...so idk what THAT was about), and she and Allura could've been bonding over their love for science and Allura could've shown her authentic Altean works outside the lions, and she'd be fucking excited bc holy shit now they both have someone outside of their respective family to yap to about science, and they aren't men good grief.
Speaking of Allura, she could've learned more about Earth and its customs. Like when she was playing those "road trip games" with the mice (Allura's funny ass would've given them a name by now) or maybe tasting some foods. Maybe they go to the intergalactic malls, and they find some human ingredients and the paladins are all crying tears of joy, and Coran and Allura are like... "but these don't move :(" and Lance is like "and god bless it doesn't girl wtf?" which leads them to have an episode about being incredibly gagged over a basic ass burger or worse dipping a carrot into some ranch.
This is also the episode where we find out who's the cooker, which spoiler alert is NOT Allura or Shiro keep those two FARRRR away from the kitchen. Lance and Hunk are the best cooks, Keith can cook, bc who else is going to feed him - the tumbleweeds? And Pidge despite being Italian has no cooking bone in her body. At best, she can cook a Fettuccine Alfredo, but that's bc her mother drilled it into her bc Pidge kept asking for more and her grandma is rolling in her grave as we speak.
Continuing with Allura, there could've been an episode about her and Coran's relationship outside "We are the only Alteans left". Like how they met, and their relationship before everything happened. Or they could've shown us how mentally jarring it is being out here without Alfor leading, bc last they checked, homeboy is fucking dead. They could've expanded the OG paladins through Allura and this one, oooo this one upsets me. We could've had it all. It has been a while since I've seen voltron, but I don't ever remember her mother having a speaking line. We just know about her father and that's just barely. We should've been able to see the connection, should've been able to see how losing her entire culture not just her family, but literally the entire damn planet is traumatizing.
She and Zarkon also barely had any type of tension, which is so odd considering he was a family friend. He was like (at least to me when I was watching and this is how interpreted it) a whole uncle to her, and was there when she was a baby. So she was not going to have any feelings besides "WE HAVE TO DEFEAT ZARKON!!" they make her out to be unreasonable sometimes, when if they just let the story breathe could explain her complicated feelings. She is technically really young and she's bound to make mistakes. I wished they just humanized that side of her more. Show us more of her and the Og paladins, give us fun flashbacks, and that the reason why she had so much prejudice against the galra isn't bc of the galra it's bc HER family's close friend betrayed them, committed genocide on her ppl and now she has trust issues.
Speaking of trust issues and also losing a father THIS is where she and Keith could've bonded. They are different in so many ways but also incredibly similar. They both lost someone dear to them, their mother is barely ever mentioned, they either have an uncle figure or an older brother figure who they look up to a lot, they can pilot, were forced into the leader role bc someone close to them "died" and have a story about their cultures. When they both thought it was them getting tracked they could've done some build-up on both sides before, so when they both sneak out it's like "Not these two idiots again, look at tweedle dumb and tweedle dumber" and they just find themselves in a pickle on some random planet. This leads them to bond as a team and to have a moment of weakness about being a leader. Keith could tell her how Shiro wants him to be the leader if something happens to him and Allura could vent to him about how hard leading truly is and that he's not crazy for a) not wanting that pressure since it's a scary adjustment to her as well but b) praising Shiro's leadership since he's a natural which causes Keith be like "oh well don't let the Mr commander act fool you he's just as scared all of us" and then they both realize somewhere in the talk that they probably shouldn't dump all the responsibility onto him and make a pact that they'll look out for each other and work together. They also realize it's been a while since they heard from anyone Zarkon, the Castle of Lions Shiro then interrupts their moment and is like "YALL WE ARE IN TROUBLE WE THE FUCK ARE YOU TWO AT" and they're like "Well looks like we're not the problem hahaha... shit how the fuck do we get back..." and then its back on the tweedle dumb and tweedle dumber bullshit literally on some cat and the hat thing one and thing two type shit. The Red lion finally comes through and is like "lord have mercy you two young fools should not be out here..." and Keith's like "Yeah we learned our lesson... sorry Red..." and Allura's like "Are we getting scolded? if so my deepest apologies ma'am, I'm sorry you had to witness that, I promise I'm quite smart " and this is when Keith finds out that red is not a dude which causes Allura (at the end of the episode or something) to drag them all (minus Pidge) about basic etiquette.
She could also bond with Shiro about being the leader, the wise one of the group, the two who can't cook but they can pilot a ship like crazy. Lance and her could bond about not finding their place on the team. Allura bc she's the only Altean besides Coran so She won't get their inside jokes and Lance bc he thinks everyone's got their own "thing".