REAL LIFE CARTOON CHARACTER

I think this is intentional — just like in "a single pale rose" pearl and rose hug and hold hands but when rose turns into pink diamond, the physical intimacy stops. that's not to say they're uncomfortable with each other, only that rose quartz and pearl seem far closer and intimate. the very first time we see pearl talk to pink she still calls her "my diamond" (which is a title used with superiors) even though this scene takes place near the end of the war and pearl has been a rebel for more than one thousand years

now let's get into the batman and alfred/robin allegory:

Rebecca and Ian, while discussing Rose’s “Batcave,” brought up the scene when Pearl couldn’t talk about Rose’s full details during “Rose’s Scabbard.” Incidentally, yes, Pearl is Alfred if Alfred was in love with Batman. It’s very important to note that we’re talking about Batman here, NOT Bruce Wayne. She loves BATMAN. 

— Steven Universe Podcast, Volume 3, Episode 1

Rose plays Batman on the ground. Pearl is Robin (and Alfred).

— Steven Universe: End of an Era, page 77

so pink diamond = bruce wayne and rose quartz = batman; pearl = alfred and rebel pearl = robin. rebecca and ian seem to want to make it clear that pearl was only in love with rose (batman). and pearl also seems to see herself as two separate people: the servant and the rebel

it makes a lot of sense for pearl and rose to create an escapist fantasy for themselves on earth as a way to get away from their awful realities. the idea that their lives on homeworld were someone else's lives was something they both took comfort in

But I've been... imagining things, even when you haven't asked me to. I imagined that I ran away and met you here on Earth, a Rose Quartz. And I'm not yours, but, I make you so happy anyway! Isn't that ridiculous?! Tell me to stop! 

Rose: Please don't ever stop! 

—Pearl, Now We’re Only Falling Apart

and that was the fantasy: pearl was a rebel who ran away and met rose on earth. rose was made on earth. pearl's presence makes rose happy even though she doesn't belong to rose.

rose is delighted when pearl shares this with her bc she loves this fantasy just as much as pearl does (and also bc it made her realize that other gems, like pearl and garnet, want to escape homeworld. she realizes that she wants to fight for them). but obviously this fantasy is incompatible with their actual lives

later on pearl would also get caught up in the idea of being rose's knight. she romanticized the idea of putting rose above all else, even herself; she romanticized the idea of having a princess to save. so she put rose on a pedestal, not because rose was a diamond, but because of this fantasy she created for their relationship

This is an Ancient Sky Arena, Connie, where some of the first battles for Earth took place. It was here that I became familiar with the human concept of being a knight, completely dedicated to a person and a cause.

—Pearl, Sworn to the Sword

in this fantasy rose quartz can't be pink diamond. rose loathed herself so this suited her just fine: she wanted to be the rose quartz from this fantasy, the gem who was made on earth and was a compassionate leader and healed instead of destroying. she thinks pearl is right to love only rose quartz bc she thinks pink diamond is unlovable

let's take a look at the movie: at first amethyst and steven think rose quartz is the solution to getting pearl's memories back. so amethyst shape shifts into rose and sings for pearl, but pearl won't stop looking at greg throughout the entire scene. then they understand that they don't need rose to be around, they need greg to disappear. so steven fuses with greg and greg disappears into the fusion, allowing pearl to finally get her memories back. greg is pink and steg is rose. when greg (pink) disappears, pearl manages to look beyond her assigned duty

it's also worth noting that pearl wasn't the only one putting rose on a pedestal. rose put everyone around her on a pedestal, including pearl, because she thought they were all so much better than she could ever be. so while pearl saw rose as a sort of princess to be saved/protected, rose saw pearl as a superior and as someone who was so much better than herself

The fact that Rose says "my Pearl" to Pearl... A lot of people wonder, "oh, she belonged to Rose". No one calls their Pearl my Pearl, people only say that to their superiors. So there's actually a lot more going on in that scene.

—Rebecca Sugar, The Truth About Rose Quartz

but this whole fantasy thing was very unhealthy and meant they never dealt with how their actual roles in gem society affected their relationship. they wanted to sweep all the ugly parts under the rug and pretend it didn't exist—and it was so easy because only the two of them knew the truth and they were all too happy to feed into each other's fantasies. it created a communication barrier between them that made it extremely difficult for them to communicate and understand each other's low self worth and insecurities. pink's final order to pearl was a way to keep the fantasy going post-war which pretty much doomed them bc pearl was unable to talk about anything she went through and rose never opened up to anyone about her past. but they needed to talk about it to heal and move forward

I believe pearlrose is supposed to parallel rupphire in this sense: both are interclass gem relationships, but rupphire never ignored how their roles in gem society affected their relationship; so much so that by the end of the show garnet's main theme becomes "the truth" while pearlrose's main theme remains "the fantasy"