> Take the hard problem of parsing a language, break it down into the much simpler problem of reading tokens, then write simple "combinators" (and, or, one_or_many, etc etc) to combine these simple parsers into larger more complex parsers.

That's a terrible example for "parser combinators beat regexes"; those are the three regular operations. (Except that you use zero_or_many in preference to one_or_many.)

Can I see the (implied) counter-example?

A regex which turns a language's source code into an AST?