As someone in the distinct minority according to the poll (and frankly, more drastic than I was expecting. Though truthfully, I suspect, those that do not use them or are not interested in them would be unlikely to read this thread or answer the poll if did), I have to say, "No. I will not allow them." and "They are obviously not necessary." as we had 20 years or so without them and the game worked fine.
Equally obvious, those of a certain mind set and/or style of play and/or were enamored with the systems in which they weren't optional [whether because it was their first experiences -and so it is "the way D&D is supposed to be", in their experience- or simply liked those editions that used them], naturally, will believe them to be "necessary"...or at least prefer them to be used in the game.
They exist to allow those people to have a game -style and flavor and system mastery- that they enjoy and are familiar with. That style is not what I enjoy or am after out of a D&D game. So, no. They don't get used.
Thankfully, 5e had the good sense to say "You don't have to. These are optional." and any kind of specialized character that can be made with a feat can by role-played without them. No, you won't get your +whatever to your shield attack or advantage on your perception check or whatever, but that is not stopping you from playing an "observant" character or someone who fights with their shield or knows some rituals. Just work it out with your DM if that let's you do something unusual in game play every now and again. DMs who can't/don't want to be bothered can say "just use the feat"...others might have some little bonus or boon of their own...or just keep it in mind as trappings/aesthetics.
Now, the other question this seems to poke at or skirt around, it's not the necessity of them in question, but the consideration of "Do they add to/are they 'good' for the game?" and/or "Do they encourage a certain play style, flavor, focus on system mastery that is detrimental, on the whole, to the understanding/experience of a Role-Playing Game of creative fantasy and imagination?"
That is, of course, a much broader question and only answered on an individual basis, with no "true" single answer, and what one considers "good" for one's enjoyment of playing D&D [or any RPG, for that matter] or not.
For me, I don't use feats. I won't using Multiclassing [as written for 5e] either. It is, also, optional (though a much more longstanding concept in the game). I know I'm in the minority (if not the Lone DM, hahaha) on that as well.