Well, for very relative values of "all-functional".

But yeah, Cabal is certainly a bit of a pain. Happily, people are working on it. Superior cabal-dev functionality is going to be integrated into cabal proper very soon, if it hasn't already, for example.

Also, couldn't you just compile your binary with static linking and just deploy that? I understand there can be problems if you depend on certain non-Haskell libraries like GUI toolkits, but that shouldn't be an issue for a web app. I think a statically linked binary is pretty similar to a jar file in practice.