Most? You think there are more than 2500 species which adult humans would say are cuter than babies? That seems wildly implausible to me; I'd say no more than 300 or so are on par with babies, and fewer exceed it. That isn't too much; surely you could list maybe not >300 species but a measly 150.

How about birds? >10,000 species there; you think there are >5,000 extremely cute birds?

I'd venture that there isn't even a bare majority of cuteness at zoos - institutions would would select for cuteness.