I mean isn't C ubiquitous enough that it is essentially language agnostic? Or is your suggestion that is should be purely pseudocode?
Even if you can write a compiler assuming infinite memory that generates programs that also assume it, it would be a disservice to readers to ignore that for brevity. It's an important part of understanding how programs are created.
I don't follow your rationale. With C the developer manages heap memory by basically calling malloc and free.
This means that once you have the memory model set, all you need to do to roll your compiler is to implement the interface.
A language that "don't require it themselves" is a language which provides only high level constructs and dumps all the memory management logic to the compiler/runtime, from object allocation/deallocation to lifetime management.
How is that simpler to pull off by a compiler writer?
Another good idea is to write a compiler in the target language.
That's why I'd like to use a language that I already know instead of learning a new one while also learning new material.