I will have to admit that as my son is approaching 20, and we watched the Potter movies when he was a kid, I'm not fully versed in what makes a 'Potter' mage. WoW Mage? Depends on the era and abilities I guess but, D&D Wizard/Sorc/Warlock, are distinct, and as 5th is evergreen for a bit here now, I dont think what you are describing is a class, its an uber-Mage.
Some of the problem is that Harry Potter magic is ridiculously OP if you're going to truly port it over directly, and if you don't port it over directly, you're looking at already adapting it, which means you're already limiting it (severely) compared to the books.
HP wizards essentially treat
all spells like cantrips, and only get tired after literally hours of continuous spellcasting. With just a modicum of training (aka, what Dumbledore's Army could cobble together just with their own efforts), you can get quite competent duellists who function more like impressively-armed
soldiers than like Hermetic wizards with tricksy powers. Spells also often have nearly unlimited range ("
Accio Firebolt!"), durations of hours to days, the ability to trivially-easily lock down enemies or end combats with a single well-struck spell, etc. While at the same time, things that are trivial magic to a D&D character are notoriously, fiendishly difficult magic. Even the simplest kinds of transfiguration and conjuration are profoundly difficult magic. Summoning man-sized creatures out of thin air is something only the most powerful and talented HP wizards can do. Performing magic
without a wand is nearly impossible for the vast majority of people. Etc.
HP magic works the way it needs to work to make an interesting book series. It is absolutely
rife with abuse potential for anyone actually trying to use it scientifically (as analyzed, IMO poorly, by the [in]famous "Harry Potter and the Methods of Rationality" fan fiction.) A huge amount of why it is so fun is that it's unexplained, mysterious, and folks just...don't
use it with all that much cleverness or subtlety in the books, apart from scoundrels like Rita Skeeter. Even Voldemort himself has a hilariously limited view of what magic can actually achieve, and his whole
thing is supposed to be power for power's sake and nothing else.
At best, a "Harry Potter Wizard" class would only limitedly approximate what HP wizards do. It couldn't be represented with Vancian spellcasting, even in principle, because Vancian spellcasting isn't compatible with the kinds of magic done--not even the Warlock model actually captures it. You'd be, effectively, building an entire level 1-20 spellcasting class that never learns anything above a cantrip...but their cantrips can become ridiculously powerful...but they can only use so many until they have to rest a bit, etc., etc. It just ends up being "I want to use a fundamentally different conception of what magic
is than what D&D has had baked into it for all but one edition."
Ironically, 4e would have no problem making a Harry Potter Wizard, you'd just reskin the Power Point classes for it, and indeed the whole "spam your best option" bug/feature that Power Point classes have in 4e would fit
even better for the Harry Potter theme than it does the Psionics theme. Hell, you can even rename "Battlemind" to "Auror" and you're already off to the races.