I think writing timing-attack resistant code in Haskell would be very hard to impossible, at least without writing very unidiomatic code (basically "C in Haskell"). I'm happy to be proven wrong, though.
In fact, I believe something along the lines of this has already been done: https://cryptol.net
Edit: Whoah, why the hate? :(
Simply put, there are easier and cheaper ways to guarantee timings. Perhaps Haskell is even capable of harnessing them. (I'm thinking of the usual "no secret dependent branches", and "no secret dependent indices".)
I could run Rust code on a PlayStation and PocketStation (although I had to cheat a bit on the former because LLVM doesn't support MIPS I).
LLVM is not as widely ported as GCC (especially on older, deprecated hardware) but it's getting there.
Until the early 90's C had hardly any meaning outside big expensive UNIX boxes.
And it was already on its way out on Windows and OS/2, if it wasn't for the rise of FOSS software and its dependency on C.
In my experience most modern codebases tend to target POSIX systems (explicitly or implicitly). That gives you a subset of C to work with and makes your life easier. The exceptions are things like DSPs which can have rather non-standard layouts but you generally write very specific and unportable code for these anyway.
Of course if you want to be completely portable you can't assume that CHAR_BIT == 8 or that you can convert back and forth between function and data pointers but in practice a lot of software relies on this.
Even before stdint became part of the standard it was very common for programs and libraries to typedef their own "sized" integer types. It's the only reasonable way to deal with ints in C IMO, otherwise you can't assume that your ints are greater than 16bits (which is probably too tiny for many uses) so you're tempted to put "longs" everywhere. But then longs will be 64bits on modern architectures which could be overkill and reduce performance.
So in theory those variable-size integer types are interesting but in practice they're basically useless because you end up making assumptions, one way or an other. I think it was a good idea for Rust to get rid of them.
The sort of direct control one might look for is, as far as I know, only practically found in your processor's assembly language, and your operating system's collection of syscalls.
I think Rust, Common Lisp, OCaml, D, Haskell, and other languages give you a lot of benefits that are simply not worth giving up in a new crypto library, like safety.