I don't experience the emotion of finding things cute, but I'd like to understand the concept at least from an analytical perspective, both out of intellectual curiosity and to better empathize with people. I may add more mana to the bounty if warranted.

First, what I do know: There's an evolutionary incentive to consider your kids cute until they can take care of themselves. Same for opposite-sex adults, although there seems to be a subtle distinction between "cute" and "hot" that I don't get. Kids have relatively large eyes, so other things with large eyes also look cute, e.g. anime characters (except for https://fma.fandom.com/wiki/Father?file=Homuncurus.jpg I've been told). Similarly, babies have soft skin, and so do furry animals, so furry animals are cute ... except by that reasoning why aren't blankets cute?

Why are miscellaneous non-baby things like architecture (https://hpmor.com/chapter/5), math (https://www.reddit.com/r/math/comments/3citj1/whats_the_cutest_proof_you_know/), adult-size clothes (https://twitter.com/search?q=%22cute%20dress), etc. also called cute? Is there a general explanation, or is "cute" actually multiple distinct emotions that English doesn't have distinct names for?