Butting in... I disagree. You can exclude any race and not really have an impact. Even humans. As you said, there are over a hundred races, plus homebrew is super-simple. Get rid of any one race and there are two or three more to take its place.
Unless, for some reason, you decide to do a thing like say "there are no mines or good smiths anywhere on this world because there are no dwarfs." Which is silly. If there are no dwarfs, then humans, goblins, kobolds, gnomes, drow, etc., would take their place and the only players who would care are those who desperately want to play dwarfs for a reason. If there are no elves, you have humans, gnomes, firbolg, and that new faery race to take the place of "woodland dwellers who are in tune with nature and the fey and makes beautiful, natural goods and is probably a bit of a snot." If you get rid of tieflings, you have drow and shadar-kai to take their place in the edgy loner club. If you got rid of dragonborn, well, there's nothing else that has a breath weapon, but you still have lizardfolk and playable yuan-ti.
D&D is a crowded system and there are probably relatively few people who would be truly horrified if your world didn't have one or more of the Core Four.