Typography can be understood mathematically to the extent that communication can be understood mathematically. You're never going to account for style, trends, or connotation.
Same with baseball, by the way. Advanced analytics can complement and enhance your understanding of baseball. But there are people involved. It will never be as straightforward as throw a curve because the count is 3 and 1 in this situation.
Human interaction is always going to be art (and fashion) as much as science.
Baseball is... I mean if a team of engineers can design a rocket that lands vertically, I am fairly certain they could design a robot that hits balls with a bat. In fact I am surprised we don’t already have robot baseball.
Typography is supposed to be perceived by human brains. So it will be subject to interpretation. Baseball is absolute: you can measure where the ball flew, where it landed, and who caught it.
It's amazing how blind to humanity we developers can be.
If you take the human out of the batters box, you're no longer playing baseball. Baseball is a game. Played by humans for the sake of competition. If you build a robot that is able to hit every ball. Guess what? There's no point in playing baseball anymore. Have you "solved" baseball? Or have you destroyed the usefulness of it?
Approaching baseball by solving the physics of the bat and ball is completely missing the point of the game.
Trying to "solve" typography is equally meaningless. There are no definite answers to be found for the meaning of Coca-Cola red or IBM blue.
You are wrong in a subtle way. Robots playing baseball would be silly and useless. Almost as bad as athletes who use steroids (ha!). But baseball is a sport. Sport and art are similar: by humans for humans is usually the winning formula.
Typography can be art. It can also be utilitarian. Most typography is. Imagine if the entire WWW used either Comic Sans or Times New Roman with 1.x or 2.x line spacing. Just no. I am willing to bet you have published stuff online (even this comment; how meta), and your publications have benefited from having good typography. Typography that you didn’t have to think about or arrange or pick out. Making utilitarian typography more beautiful is a benefit to everyone. If only a select educated and experienced few could use beautiful typography because it was an arcane art, as you seem to want it to be, then well, we’d be using Comic Sans. If using more advanced mathematical models results in 99.999% of the readable web being more beautiful, I am for it. It doesn’t preclude someone from doing work by hand to either stand out more or to create art. But it certainly would be good for everyone if more advanced models existed. This is the same as how it is better that we have Google Fonts as opposed to every website owner having to create or commission a from scratch font.
I agree that the number of data points needed for study and the number of variables involved are both key factors. The one area that comes to mind where a approach might be easiest is closed platforms like the hardware Kindle reader -- for example, measuring read times by a large population of the same text, with varying fonts, on the same hardware. Improved typography might reduce read times some modest percentage over baseline due to improved readability.
Same with baseball, by the way. Advanced analytics can complement and enhance your understanding of baseball. But there are people involved. It will never be as straightforward as throw a curve because the count is 3 and 1 in this situation.
Human interaction is always going to be art (and fashion) as much as science.