Arguably the scalar focus of CPUs is also to make them more suited for C-like languages. Now, attempts to do radically different things (like Itanium) failed for various reasons, in Itanium's case at least partially because it was hard to write compilers good enough to exploit its VLIW design. It's up in the air whether a different high-level language would have made those compilers feasible.
It's not like current CPUs are completely crippled by having to mostly run C programs, and that we'd have 10x as many FLOPS if only most software was in Haskell, but there are certainly trade-offs that have been made.
It is interesting to look at DSPs and GPU architectures, for examples of performance-oriented machines that have not been constrained by mostly running legacy C code. My own experience is mostly with GPUs, and I wouldn't say the PTX-level CUDA architecture is too different from C. It's a scalar-oriented programming model, carefully designed so it can be transparently vectorised. This approach won over AMDs old explicitly VLIW-oriented architecture, and most GPU vendors are now also using the NVIDIA-style design (I think NVIDIA calls it SPMT). From a programming experience POV, the main difference between CUDA programming and C programming (apart from the massive parallelism) is manual control over the memory hierarchy instead of a deep cache hierarchy, and a really weak memory model.
Oh, and of course, when we say "CPUs are built for C", we really mean the huge family of shared-state imperative scalar languages that C belongs to. I don't think C has any really unique limitations or features that have to be catered to.