The problem is "witch" is surprisingly nebulous. A witch is myth, literature, culture, and religion can be.
An adherent to some "green" form of magic; tied to the natural world and akin to druids (and indeed, nearly interchangeable with) - something akin to modern Wiccans*
A wise woman, healer, herbalist, or folk-magic practitioner - Hedge wizards
A black or evil caster who sold her soul to the devil - Salem witches, Halloween witches
A fortune teller, omen-reader, and layer of curses, hexes, and such - Macbeth witches, voodoo priestesses*
A hag that lives alone and eats children - Hansel and Gretel
Another name for a female magic-user - Harry Potter
* Common conception of religious practice; not intended to generalize or make assumptions about anyone's beliefs
That is a LOT of ground to cover, and to be honest some of it is already handled by other D&D classes. Hags, druids, wizards and warlocks cover about 90% of that. I could see a new subclass or two (warlock and druid seem likely candidates) and maybe a decent background (and some new spells, of course).