Those regexes that are ubiquitous are called regular expressions because they describe “regular languages” (qv), which are recognized by nondeterministic finite automata, which are converted to deterministic finite automata by fun with powersets, which are compiled into software state machines behind the abstraction of the regex libraries.
So they are not at all rare but not exposed to programmers explicitly.
Almost all "regexes" in programming languages are not actually regular expressions and do not have the properties you describe. (I'd argue that this is one of the clearest demonstrations that programmers do not put a lot of value of state machines)
Yes definitely a different thing when talking about ‘extended regex’ libraries, wrt to the regular languages (language class) and associates recognizers.
So they are not at all rare but not exposed to programmers explicitly.