IMO the biggest problem with regexes as seen in the wild is a lack of composability. If you need some kind of pattern like "[setA][setA+setB]{0,n}" then you'll copy-paste the definition of setA in both places. If you need to re-use that entire regex you'll copy-paste it again and construct a monstrous string with a really well-defined structure that isn't even slightly apparent without a reverse engineering session.
Up to a point you can solve that by just giving names to relevant sub-expressions, using a regex builder, etc, but in my experience if I'm going to write even a moderately complicated regex I'll probably be better served with something like parsec (a python implementation here [0]) in whichever language I'm currently using.
That isn't to say that regexes don't have their place -- anything quick and dirty, situations where you need to handle unsanitized input (mind you, the builtin regex engine is probably vulnerable to exponential runtime attacks) and don't want to execute a turing-complete language, etc.... I just think it has bad ergonomics for any parser you might use more than once, and I haven't yet regretted using parsec in situations where a complex regex would have sufficed.
Perl is great for this. It’s been a long time since I’ve written any, but with the right flags and use of qr// you can write extremely readable perlre.