In practice, functional programming is a way of organizing imperative programs. Kind of like how OO is a way of organizing imperative programs.
Almost all applications written in Haskell use the IO monad quite a bit, for example. Large Haskell projects generally use a lot of C libraries, and sometimes even directly include C code for performance sensitive bits.
I don't agree at all!
Haskell is extremely pleasant for imperative programming. There's a learning curve for sure, but you get a lot in return. (STM is one small example). I would much rather write imperative Haskell than Python.
It does gets messy when you start writing really low level code (direct pointer manipulation, etc). And it sucks for small scripts (too much project boilerplate, small standard library). But those are the only real pain-points.
You can very successfully keep nearly all IO at the edges and do the heavy lifting in pure functions if you make it a goal.