Tangentially: the only reason OP is able to "stop looking at assembly" is because a bunch of other people still do. There are compiler codegen bugs constantly, but OP never knows about them because other people who do read ASM find, report and/or fix them before they cause too many downstream problems.
Another way to say this is that the "compiler" does not "get it right". A ton of people, constantly reading the ASM that the compiler outputs, work together to "get it right".... eventually :)
So the proper way to look at this is, if you've stopped reading ASM, that's not because codegen was solved, but rather that you have implicitly decided to outsource to other people the problem of keeping codegen working reliably.