Rainy Saturdays

First, starting to learn magic at 11 is total rubbish. Using Avatar: The Last Airbender as an example. Learning magic at 11 is comparable to someone learning they can bend at 5 but they don't start training until 11. Or someone in our world has prodigious abilities but they don't train until high school. Do you see how dumb this is?

So in the meantime, wizard kids have this power that they can't control properly. It's not that big of a deal if the kid has a magical family but what about mugglebornes like Hermione or kids who grew up in muggle families like Harry?? Harry was literally a hazard to the Dursleys in more ways than one and it's understandable, not excusable, that they hated him.

Plus Hermione's character is annoying due to her role as an exposition device. It's tiresome that a muggleborne girl is constantly showing up purebloods who literally grew up around magic. As the books go on, she takes over Ron's role in the trio as the magical common sense guy. In reality, mugglebornes should be at a major disadvantage. Let's say I am trying to learn Spanish. I have no Spanish-speaking family. And let's say I end up in a class of immigrant kids whose parents all speak Spanish. They may not be fluent themselves but they have a huge headstart on me. In time I will catch up to them, especially if I work hard like Hermione, but initially, I would perform worse than them. As first years, the pureblood and halfblood kids should be blowing Hermione out of the water. If not for the entire first year then at least the first semester/term.

So how would I fix this issue? Four ways:

Magical kindergarten/elementary school

Hogwarts should be a highschool/college level institution. Or maybe Hogwarts could have different school levels. Kids should learn the introductory concepts for Charms, Transfiguration, Potions etc in primary/elementary school or even from their freaking parents. Ron's intro scene with that make my rat yellow prank spell was just sad. And having Hermione call him out for the spell not being real was just more salt in my annoyance. As kids, they learn the basics like wand movement, magic theory and safety. And basic spells.

Advanced learning

When they go to Hogwarts they should focus more on application and higher levels of theory. For example: Magical Ethics (what are the moral boundaries of magic **cough**rapedrugs**cough**polyjuicepotion**cough**), Magical Research (do projects/experiments to learn more about the nature of magic, like how is elf magic different from wizard magic), Spellmaking (why is Snape the only dude in HP inventing spells!), Improvised Spells (like in Wizards of Waverly Place), Magic Economics (how does magic work with the concept of scarcity, what is scarcity in the wizarding world), Magical Defense (not just against the dark arts but basic defence like self-defence in our world and perhaps survival skills) etc. They should learn non-verbal and non-wand magic as well of course. Maybe this could be taught at the end of primary school or the beginning of Hogwarts. Instead of the very end of their Hogwarts education.

Accessible classes for mugglebornes

So what about mugglebornes, you say? Well, there are two options. You can provide after-school classes for muggleborne students to learn magic before they attend Hogwarts. Think of extra lessons or night classes in our world. Or you can send the mugglebornes to summer school(s) before Hogwarts which leads me to my next point.

Different Class Tracks

Put muggleborne kids in a different class track from the purebloods/halfbloods who went to magical primary. Like how we have advanced classes for students who are super bright or slower-paced classes for students who need extra help. Students like Hermione would gradually graduate to the advanced track while lazier students like Harry may stay in the slower track. Or maybe bright students like Hermione could do placement tests to get into the advanced track from the start. Some pureblood students could even be demoted to the slower track if they begin to goof off (maybe Ron) or need extra help (maybe Neville). And you can mix and match! So Neville would be in Class 1 Herbology but Class 2 Potions :). Maybe Harry would be in Class 1 DADA but Class 2 Potions etc.

If lack of teachers is an issue, then pureblood families would teach their own kids and the primary school would be exclusively for muggleborne kids and/or pureblood/halfblood kids whose parents can't provide tutoring.

Conclusion

So yeah, that's how I would revamp the school system. Hogwarts is a weird school. Like students leave as adults but leaving Hogwarts feels like leaving primary school. I never felt prepared for the world after highschool but at least we have college/university. Even if HP has trade schools/apprenticeships for jobs like healing and being an auror, I think their magical education is seriously lacking. And the spellwork in HP is honestly very lame. Wands just end up being like guns. More battles should be like the Voldy vs Dumbles fight in book 5.