Stuff like this makes me feel so neurotypical. Really. I can have a sprited argument about the benefits of the K&R brace style, for example. But often I see articles about "ugly" vs. "beautiful" fonts and the difference, to the untrained eye, is so minute as to be just technical.
Would you say that about really well-edited scene in a movie, or a photograph that feels perfect, or a joke with perfect delivery?
A lot of those things are defined by timing and the space between moments that aren't exactly fully rational. And, if they're doing it well, they make you feel something, even if you can't describe exactly how they're doing it.
A "beautiful" font is like that. The font itself is not beautiful on its own, imo; it's raw material. The beauty comes out in how it's used, when you can look at A or B completed thing and say, oh yeah, B feels "better," but I don't know exactly why. It's not just because of the font, but the font 100% matters.
I think it depends what field you are in. In printing and publishing, these font differences can create major issues, such as in formatting and readability. You are right, it is not an exact science and can be subjective, but it is important in some instances. Differences in fonts can affect the entire layout of a page. I was watching a video discussing some font and logo design within the Alien franchise, and some of it worked on a level which was very subtle but I believe effective.