You absolutely can write void _start(void) and as long as you finish using exit() everything will work just fine. I've written some super small programs this way (on the order of few kilobytes) which don't interface with system libraries in any way.
That'll work on some systems and not others. Whatever compiled and linked your C arranged to _start to be at the place the instruction pointer starts from. Setting up your own stack from C is dicey but sometimes the default value for the stack register is usable as-is.
I tend to go with ffreestanding and the crt*.o for the platform instead of going from _start directly but sure, you can write whatever startup code your platform wants yourself and link with -nostdlibs or similar. Some platforms are OK with just the address of the entry point burned into an elf. Compiler test code sometimes looks like that.
