Might we run out of Unicode code points, like we (seem to) be running out of IPv4 addresses? As another comment mentions, once you add all these snowmen, with/without snow, male female and gender-neutral, in a few skin colour options (plus neutral)... it adds up. Plus, exponential growth once you consider family of snowmen (different number/genders/races of "parents", different number/gender/races of "children" and s…
It really, really doesn't.
According to UTS #51, as of unicode 14 (and its ~140000 allocated codepoints) there are under 3500 codepoints classified as emoji.
And do keep in mind that #, or ®, are classified as emoji.
And incidentally, U+2654 "white chess king" (♔) was in unicode 1.0. The moral panic around emoji is really tiring, it's absolute, utter nonsense, every single time.