"I don't know if one should have 'proper documentation' for a compiler."

Of course you must!

It must tell you things like:
* Implementation-specific features; eg, support for target specifics like the 8051's SFRs, different address spaces, limitations, etc;

* The calling conventions & internal data representation - essential if you want to interface to assembler or any other language;

* specifics of the supplied runtime support;

etc, etc, etc

"when you've seen one (C) compiler, you've seen them all."

Nonsense! Especially in the case of cross-compilers for embedded systems!
eg, the Keil C51 manual tells you (next to) nothing about the standard 'C' language - it assumes you know all that! It is (almost) entirely dedicated to the specifics peculiar to the particular implementation & target.