It just feels and reads a lot worse than doing it in say Python. So you could make a program clearer by writing the functional parts in one syntax and the imperative parts in another syntax.
Also, I'd like second the other posters suggestion that most Lisps have many ways of writing imperative code and that it really is no different than your average C-like in that respect.
Do you have any other examples of a production quality parser done with parser combinators?
The Lisp parser I was thinking about was Julia, which is bootstrapped in femtolisp. It looks like straight imperative code in Lisp to me.
I'm mainly concerned large parsers, like bash, Julia, Ruby, or C. You can write a small parser with any technology. FWIW I have a lot of posts about parsing here, towards the beginning of the blog: http://www.oilshell.org/blog/
EDIT: What's the benefit of parser combinators over recursive descent in Python or say Java? Is it just that it's point-free so you don't have to explicitly pass the input around?
I suppose if I saw the same parser written in parser combinators and recursive descent it would be easy to tell what the benefit is, if any.
https://github.com/meric/l2l/blob/master/l2l/lua.lua#L429
The parser generated is recursive descent.