I would like to see a witch class do things that the other classes cannot. I think there is plenty of room given the roles that already exist in 5e, for a class with a new role.
Aye, there's the rub. And the question is, are those "things that the other classes cannot" do
mechanical or
flavorful? In some ways this is the psionics debate, right? The spellcasting system can be refluffed for psionics, but many posters felt that if that's all it is then it's not really psionics.
So maybe, to pick an example, Witches derive their powers by befriending/manipulating some kinds of spirits (or demons or whatever). That's the fluff. What's the mechanics? Spell slots?
Or we could come at it from the opposite direction. Start with some kind of design idea....maybe "no spell slots, only cantrips and invocations". Then let's apply that to a Witch class.
But...is that mechanic really Witch-like, or are we hoping that it eventually becomes Witch-like because people get used to those rules?
As an example, when I came back to D&D after skipping 3e and 4e, I discovered...much to my surprise...that people felt a Warlock class
had to have "eldritch blast". It was so iconic as to be a requirement. Without eldritch blast, it wasn't a Warlock. This struck me as totally arbitrary and asinine and not even remotely related to the theme of "deriving powers through a pact with a powerful patron". Really just another blast spell with some fluff. Some random demon can grant this power to its warlock minions, but not to its own priests? So all the gods and demons and extra-planar beings and fey lords and everybody else just kind of agree...maybe at the annual "Pan Planar Conference for Might Beings"...to only give this ability to a certain class of followers? Maybe as some kind of running gag? It's dumb. But, there you have it.
So maybe we should stop worrying about what the true essence of a Witch is. All that's needed is some interesting new mechanics that would be fun to play, some fluff to make those mechanics fit various witchy archetypes, a few subclasses to build out those archetypes, add to the cauldron, stir, let simmer for a couple years, and badda-bing-badda-boom....iconic Witch class.