Most of the problem with writing early startup code in C is, in fact, the absence of a properly structured stack. It's worse than just not being able to make function calls. All of a C compiler's generated machine code assumes the existence of a stack, pointed to by the ABI-specified register, that can be used for scratch storage at any time. Changing this assumption would be so much work as to amount to a complete second "back end" for the compiler—way more work than continuing to write early startup code by hand in assembly.
Early bootstrap code, bringing up the machine from power-on, also has to do a bunch of special operations that can't usually be accessed from C, like configuring interrupts and virtual memory. And it may have to deal with the code not having been loaded at the address it was linked for, or the relocation table not having been processed, or other similar problems; these also break pervasive assumptions made by the C compiler (e.g. that it can inject a call to memcpy
whenever it wants).
Despite all that, most of a user mode C library's startup code will, in fact, be written in C, for exactly the reason you are thinking. Nobody wants to write more code in assembly, over and over for each supported ISA, than absolutely necessary.