Whoever came up with them has surely been given the same honorary place in hell with Jon Postel, who invented the utterly disastrous "be liberal in what you accept", that has plagued all web developers for the last 20 years.
Regular expressions are just a notation for expressing a finite state automata that recognizes a regular language: if that's the problem that you have, regular expressions are definitely the tool you want to be using. For instance, I recently made myself a small tool to compute the min/max/expected value of a dice roll; the notation for such a thing forms a regular language that can be expressed as follows:
non_zero_digit ::= '1' | ... | '9'
digit ::= '0' | non_zero_digit
integer ::= non_zero_digit digit*
modifier ::= '+' integer | '-' integer
roll ::= integer 'd' integer modifier?
I agree that regular expressions are often used in contexts where they should not, especially when people start using back-references to recognize non-regular languages, but don't throw out a perfectly good tool because sometimes it is ill-suited.
It's quite an amazing problem to have honestly because it really shouldn't be a problem to create a proper implementation. You can learn the theory behind regular expression in a few hours and know pretty much everything there is to know.
Without fuzzing, it's going to be pretty difficult to come up with enough test cases to thoroughly test a regex.
As proof, I submit some email header parsing code which I rewrote as a well-commented Regex which was something like 300x faster than using the Mail gem: https://github.com/pmarreck/ruby-snippets/blob/master/header...
Once you know what to look for re: catastrophic backtracking, you know how to avoid it. This is called programmer skill.
... is a part of so-called unix philosophy, the CAUSE of the internet. The fact that many web developers forgot to become a programmer is just a fun fact changing nothing.