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.)
Yes. Your Witch is either an Artificer (Alchemist) or a Monk (Way of Mercy).Are there any 5e brewing rules that give potions with a wide range of effects (beyond just the list of options in the DmG)?
I quite like the Warlock as the witch class. It doesn't get more witchy than making a pact with the devil in exchange for powers.Warlocks are witches, but there should be an extra witchy subclass that attempts to capture the classic witch tropes. The new Witherbloom subclass seems like a pretty decent take on that concept.
In 4e my favorite witch, malediction invokers (yes divine casters)Witches should be Divine Casters.
In the current edition arcane/divine divide is just one fluff sidebar so it doesn't really matter.Witches should be Divine Casters.
Being divine generally implies access to healing magics... which does make some difference in function.In the current edition arcane/divine divide is just one fluff sidebar so it doesn't really matter
Bard? Yes, (some) witches should definitely get healing magic, (Witherbloom allows that) but whether they are arcane or divine or whether that's even a distinction that exist is a matter of setting lore.Being divine generally implies access to healing magics... which does make some difference in function.
Pact of the Blade Hexblade Warlock is my go-to 5e Gishy.I don't think is quite true. You grab agonising blast and hex and you're good to go. Sure, you could improve it further, but you don't really need to, with these you will be doing pretty horrid damage.
I really wish there was an easy way to support more varied builds. One thing I did was to let agonising blast (renamed 'agony') to apply to all cantrips, which makes it slightly less idiotic to use cantrip other than eldritch blast, but that still is the best cantrip and comboes amazingly with hex. One thing I considered was changing eldritch blast so that multiple beams aimed at one target become one beam, but that seemed like a too drastic nerf. (I.e. instead of 3 x d10+Cha+hex you would have 1 x 3d10+Cha+hex.)

(Dungeons & Dragons)
Rulebook featuring "high magic" options, including a host of new spells.