I was an experienced asm programmer before a friend loaned me a copy of K+R C. I understood C immediately. I imagine trying to learn C without knowing assembler would be a much tougher road.
Knowing C also helps in understanding a lot of other languages.
The first thing learned with assembler is pointers and addresses. So I don't know how hard it would be to get them coming from other languages.
But I did first learn to program in Basic and Fortran, which gave zero insight whatsoever when subsequently learning assembler. I was pretty baffled by it for a while, until I suddenly "got it".
It helped that on 8 bit home computers BASIC was the OS and systems language, exposing the whole hardware, including having pointer like mechanisms, via PEEK, POKE, DATA, USR, PTR, among others.
Diving into Z80 was a matter of performance, not additional features.
Knowing C also helps in understanding a lot of other languages.