On the whole the choice of commands available in math mode goes back to Don's original idea that the syntax for those commands should be easy to communicate (over a phone). Or say verbally in general. And translating the visual to a sequence of words you do not really think in long-range structures that require you to keep track of a brace (argument) level to understand what a closing brace signifies.
This explains (I think) also the somewhat questionable choices like providing
\over that are actually technically a mess to implement as in
$a+b \over 2$ the
\over is suddenly changing the state of earlier material. And as you can see Leslie tried to change that by introducing
\frac and amsmath introduced
\binom and the like because they thought that those are sensible standalone constructs with names that can and should be called out as such.
But I must confess that personally for parentheses and the like I think it is much more readable to see them visually in the formula (whether or not with an additional
\left/\right attached) compared to having a long-range command with one argument where I have difficulties to see what is the starting point.
Furthermore if you do not use
\left/\right but explicit sizing like
\biggl etc. then these can come up on their own which again is an advantage in many cases.
But others might see this differently and as it was pointed out it is simple enough to provide your own structures that offer those on a command basis.