From a game design standpoint, "witch" occupies a much clearer conceptual space than "sorcerer" or "warlock" does and is more immediately familiar and understandable to a new player and the general public than almost any other class. (The general public will give you a blank stare when you mention "cleric" or "druid," for example.)
It might be that witches should have been introduced decades ago, and they've been elbowed out of the picture by this point, but they're arguably one of the biggest concepts in fantasy pop culture that doesn't have a clear specific analogue in D&D. (And no, "you can play it if you take something named something else and then adjust it in several ways a newbie wouldn't know how to do" isn't the same thing.)
For myself, I would prefer it be either a core class (replacing the sorcerer, perhaps, which has really lost a lot of its reason for being in 5E, with the wizard and warlock dividing up its 3E role) or as a PHB-level subclass of either the wizard, warlock or druid.
My wife is playing a transmuter hexblood, which is as close as she can get as a relative D&D newbie to capturing a classic Wizard of Oz wicked/Halloween witch vibe. It's not tremendously satisfying, honestly, so I might see if she's interested in playing a Witherbloom wizard instead. (She's got a real bias against druids after playing EverQuest.)
My issue with this idea is that which witch is which?
That is to say, what measure is a Witch?
Witches are like Trolls: while in continuity with one another, most depictions are in complete discord from each other (All Trolls are Different, so are All Witches). You can list a line of iconic witch tropes and I could list dozens of fictional or folkloric witches that break several of the tropes you have, or even lean into antithetical tropes.
Witches differ from each other most specifically in HOW they came into their power. D&D classes often share overlaps in conceptual space of what their power is and what it does, but rarely overlap in where it came from - how did I get from background to Level 1 class member? If the members of a class got their core powers in completely different ways, are they really the same class?
This is like the classic Magic Warrior trope - most people agree that it needs to be in the game, but nobody can agree what it looks like. A lot of people wanted a half-caster arcane magic user with access to a subset of fighting styles to parallel the Ranger and Paladin, but beyond that nobody could agree what it should look like because the origins of power for Eldritch Knights, Hexblades, Blade Bards, Bladesingers, Battle Smiths, and Wild Magic Barbarians are very much quite different. These belong as subclasses of various classes, showing what those classes can do with a little bit of arcana or a little bit of martial training gives them, rather than to a skeleton class with no unifying identity.
This is the same problem that killed the Mystic class - it was a skeleton on which various Psionic tropes were hung as subclasses that owned 90% of the meat and potatoes.
Witches are similar in nature. You've got studious wizardlike Witches like Hermione who studied really hard but also had to have that magic spark to begin with. Then you've got the historical Christian interpretation of witches who made deals with the devil. Then you've got fairy tale witches who are represented by Hags and other Fey creatures in D&D and might be better represented as a lineage than a class. You've got characters like Sabrina the Teenage Witch who is only half-witch and thus half a member of a witch species - suggesting an inheritance factor for some stories. You've got Wiccan adherents that treat witchcraft as a nature religion. You've got Mahou Shoujo who are just as likely to learn their magic from scratch (anyone can access it with the right teacher) as they are to inherit their magic. And you've got some witches like Kiki of Ghibli fame who need to maintain a belief in themselves and navigate her developing emotions and hormonal changes to maintain her powers as they slip away from her (initially she believes it's because she got distracted from doing witchy stuff).
As you might notice above, any and ALL of the spellcasting classes are reasonable choices for a witch character. That's usually a sign that a new class is not needed but rather that this is a very broad concept that is better applied as individual subclasses of various classes. See Ninjas - we have both Way of Shadow Monk and Assassin Rogue.
Alternatively, they could develop Witch subclasses that work for Bards, Druids, Sorcerers, Warlocks, and Wizards, much like the Strixhaven subclasses do. This may actually be the best solution. Do we think that the Strixhaven subclasses already serve this purpose pretty well?
