Compilers is not an important topic because there's nothing universal you can take out of it. Machine code as we know it is a pretty arbitrary construction. Register machines themselves are pretty arbitrary---they're just one way to make use of transistor circuitry. The conversion from C to machine code is not really worth remembering. It's true that this system forms the basis for all our computing, but like the nanoscale physics of semiconductors, it's not required knowledge for programmers. It's just a bag of rules...it's not even a bag of tricks.
If you work at Intel optimizing compilers, then maybe you need to know this stuff. If you never hunch down and program inline assembly, why do you care? You're too far from the bytecode to leverage compiler knowledge against performance, and in fact you'd probably be wasting your time to do so. Its workings operate below the required level of abstraction. Understand what's going on, but leave the details to someone else. I don't need to know how Firefox implements an HTML parser to render my webpage. I just need to know that it does so in a consistent way.
Compiler implementations are pretty arbitrary, and oftentimes they're filled with a lot of goofy stuff. We shouldn't still be carrying cruft like Please-Excuse-My-Dear-Aunt-Sally around in our languages---and this is half of what a compiler does. If there's anything beautiful to take out of a compilers class, it's that a compiler can compile itself. There---I've spoiled the ending, skip the course and take a theory class instead.