The [...] exceptions just prove the rule
That's a semantically empty statement :-) And an exception can only be
an exception /to a particular rule/.
Mathematical layout has all sorts of little idiosyncratic rules about
spacing etc. that are subtly different from regular text, even though
many characters can occur in both environments. That's why
high-fidelity math layout needs to first identify those areas of a
document where math layout rules apply. In TeX that's handled by using
$ as an operator, in other environments other conventions (including
out of band styling) are used.
\( ... \) is the modern alternative to $ ... $; this has to do with
parsing (incl syntax highlighting) and error detection.
The funny thing is that (La)TeX actually requires a good number of
manual adjustments to produce good math layout. The relevant knowledge
is hidden in books like "More Math Into LaTeX" or "Mathematics into
Type"; the former is quite thick in fact.
Stephan