[jks]

> it seems not a huge computational task to figure out that ] is a `\right]`

TeX's design was finalised in 1982, when the computational resources were different by a few orders of magnitude. There is a very strong culture of backward compatibility (search for "A torture test for TeX") and there are so many equations written in TeX documents that it would be impossible to change the parsing now.

That said, something like MathJax would be free to create their own TeX-like syntax where parentheses are automatically paired.

I for one often find myself wanting more control, writing `\bigr]` or `\biggr]` instead of `\right]` to get the rendered equation to look good.

> And while rendering `(a+b)/a` as a `\frac` is opinionated, honestly, the only reason why this occurs in my notes is when I was too lazy to type `\frac{}{}`.

Plain TeX has the much nicer syntax `{a+b \over a}` but for some obscure reason LaTeX recommends against that.