Why handwritten, or why using a parser combinator framework?

Handwritten parsers are most commonly used because most tools have problems making things like proper error reporting good enough to be worthwhile.

Parser combinators is really just a fancy way of composing a parser from higher order functions instead of writing out a function body. If well done it basically provides a DSL to build the parsers, and the way this works by composing small fragments is pretty much what we do with recursive descent anyway, so it's a good fit.