• No limits on how often you can cast spells
• No explanation of how magic actually works
• No explanation of how magic objects are created
• No explanation of how spells are invented
• No explanation of how different species' magic differs
• All the spell names are silly words in English and poorly understood Latin
• Never explained why incantations or gestures are needed
• Never explained what makes spells other than Patronus hard or easy
• Never explained what makes a wizard powerful other than "they learned a lot of spells"
• Few/no limitations on spells, or limitations aren't explained
• No contextually dependent spells
• It's impossible to predict what will happen in the books based on understanding the magic system
• There are just. no. rules.

Brandon Sanderson is the best magic system writer in the world, and these are his "laws of magic" for creating an interesting magic system:

The First Law

Sanderson’s First Law of Magics: An author’s ability to solve conflict with magic is DIRECTLY PROPORTIONAL to how well the reader understands said magic.

The Second Law

Sanderson’s Second Law can be written very simply. It goes like this: Limitations > Powers
(Or, if you want to write it in clever electrical notation, you could say it this way: Ω > | though that would probably drive a scientist crazy.)

The Third Law

The third law is as follows: Expand what you already have before you add something new.

Rowling never follows these principles. The reader doesn't understand the magic, magic is rarely given sensical limitations we understand, and Rowling always adds new stuff instead of explaining what we already have.

I posit that the answers to all these questions I listed just don't exist. There is no explanation. Hermione does well in school because she rote memorises. Harry and Ron can't engage with the material in their homework because they don't understand it because nobody does.

What Harry Potter's magic system, insofar as it exists, does do well, is vibes. It feels like a wondrous magic system. That's what sold books. Harry likes all the vibes stuff in the books, like the spooky castle, fighting evil, being a strong wizard. He doesn't understand any of the magical theory, because it doesn't exist.