The reason I bring it up is that UTF-16 is a very commonly used internal encoding for strings, and regular expression engines for platforms which use UTF-16 internally are generally designed to work on that encoding without conversion to UTF-32. Examples that spring to mind are most JavaScript regular expression engines, the ICU regular expression engine, and java.util.regex. If variable-width encodings were so difficult to deal with then you would expect these to have run into some problems with it; however, as far as I can tell, they have not. This is evidence against variable-width encodings being difficult for regular expression engines to deal with.
(Sanity check for my argument above: If you read through https://swtch.com/~rsc/regexp/regexp2.html, which covers both backtracking and non-backtracking regex engines and includes code, none of the code examples would need more than trivial modification to deal with variable-width encodings.)