See, based on the title, I thought this was gonna go in a very different direction. That is...my big problem with Wizards is that none of their mechanics actually mesh with their theme.
Sorcerers clearly have a physical tie to their magic. That's why they can literally grow wings (for Dragon sorcerers) or other fun things. Warlocks? Between the Pact/Patron divide, Invocations, and their unique approach to magic, they feel different, though I would of course like some even stronger flavor elements if possible. Bards are the ultimate versatility class, capable of being second-best at nearly anything, and pretty decent at most things. And they actually Inspire people, and actually soothe them with song or story (Song of Rest).
But Wizards? Wizards don't actually do research, it's all just handwaved. Wizards don't actually study much of anything, it's all implied and insinuated. "Oh, the new spells you got are ones you were researching," some say, but that justification applies to any class that gets spells. By those lights, a Bard is superior at research, since they can acquire spells Wizards never could.
It has always bothered me greatly that this is the case, that the Wizard's identity has been effectively offloaded entirely to its spell list and the fact that it can learn spells from scrolls. I truly, deeply wish they'd given Wizards more research-, study-, and academia-related benefits. As it stands, they're very nearly devoid of the one explicit flavor component the class is supposed to have. It would be like having Fighters that mostly don't make attack rolls due to all their abilities inducing saving throws. Or Clerics that never actually do anything religious, other than calling their spells "prayers."