If your code depends on a bunch of initialization from libc, then you should continue to link to and use libc. sp.h can coexist with libc just fine; if you link to it, the library makes sure to conform where it needs to (e.g. not stomping on the register that holds the TLS base pointer).

What sp.h does not do is reimplement all of libc's initialization code. If you want to build a freestanding binary, there are a few utilities in there for defining a _start so the loader can actually jump to your code. But it's not, and isn't meant to be, a libc replacement in this sense.