The are similar to BNF notation and the like, the basis of many a good language specification. So it makes sense that notation like this would be used in lexers to indicate classes of expected characters. The base symbols really aren't that cryptic.
Then I think there was the UNIX-do-all-you-can-in-a-single-line idea that took over. After improvements in sed and grep scripts, regexes acquired new powers but shorthand denotations for them. Larry Wall incorporated them into Perl as a general tool for parsing text. I'd guess it retained compactness for the oneliners that still were important with perl. And there were shorthand names for common character classes, and even more power was asked and given to regexes. Of course, since Perl was also a language of modules, the regex syntax also worked in blocks of statements and it leveraged syntax that was more widely known.
Their incorporation into Java is really what made people look at them, IMO. Java did nothing to accommodate them. And as a result, expressions with backslashes of moderate difficulty turned into dense jungles of backslashes. Java gave regular expressions a new market if you will, but it their most atrocious form. If you've seen those, and paid no more attention, you might think that the regex is a Thing That Should Not Be.
It's interesting that given a clear enough syntax, for Ambrose's verbose version, somebody could come up with a module for Perl that could take the verbose regex and "compile" it into a compact regex that Perl understands, using simpler regexes through overload::constants or possibly a Parse::RecDescent grammar.
