I may be reading this wrong, but it appears to rely on trusting at least one (if not more) of the other compilers to not be compromised as well.

Given that so many modern compilers can be traced back to GCC or LLVM these days, this requirement would seem problematic.

EDIT: As pointed out below, it would take a nearly AI level compromise to protect against this kind of attack, but at a theoretical level it would be possible.

Of course, if you control the GCC compiler, you control the Linux Kernel, and no programs run on Linux that don't rely on the kernel for reading and writing files...

It does not rely on you trusting any of the compilers to be uncompromised. It relies on you trusting at least one pair of the compilers to not be identically compromised.

At a theoretical level, it wouldn't be too difficult to write a C interpreter from scratch, with enough simple obfuscation that detecting what it is interpreting really would start looking like strong AI.

And even if such a sophisticated program were written and somehow managed to not take up too much CPU time, it would at least probably result in rather large binary size increases in whatever it's injected into... even Linux isn't so big that a few hundred kilobytes wouldn't stick out like a sore thumb.