Fortunately, you don't have to use C for this any more. Rust has bindings for making extensions for Ruby, Python, Lua and Node, and generally it's very well suited for making zero-cost cleaner APIs on top of C FFI.
Depends on what you are doing. You often need to pull in the other language's runtime while libc is typically already in use. You also have to be careful about ABI details like string representations, concurrency, and threading features.
Node is actually a bit lack luster to write extensions for in C, as it prefers to go through v8's C++ abi. Same for LLVM: they have a half baked C interface to what's really a C++ abi. There's an alright attempt at allowing for Rust bindings in node: https://github.com/neon-bindings/neon
Because C is so raw bone, highly generic APIs from higher level languages can come off as rather lackluster when reduced to C's world view
Want to build a library that can be used in any of the high level languages? Write it in C and provide binding.
A library code written in PHP can't be used by Haskell. Not without a big overhead. Or vice versa. Write it in C and your are done.
These are where C still comes handy.