Properly compiled and built C programs run just fine, for the usual C definition of "just fine".
C compilation requires the presence of a C compiler or ilk, same as everywhere else.
You can use Xcode (which includes the IDE and the command-line tools including the Clang C compiler), or (just) the Xcode command-line tools (without the IDE), or can load a compiler of your choice using Homebrew or otherwise. Clang, gcc, pcc, and various other C compilers are around.
Homebrew has gcc and LLVM available, and both of which are... large. I haven't confirmed the LLVM build includes Clang, but I'd expect it does.
You could also use the Emscripten C compiler too, and compile your C code into WebAssembly and run the code directly in a web browser with WebAssembly support.
And Microsoft Visual Studio Code IDE is around, but I'd expect that needs the command line tools.
I find using the Xcode IDE makes C work faster and easier.
Yeah, there are inherently trade-offs with an IDE or any other tooling.