Since the compiler is in charge of generating the layout of the executable, it's in the perfect position to alter it so slightly to patch in a backdoor.
I don't care where your compiler's AST tree or code generation is. For any compromised program (including a compiler) all I need to do is to monitor the files it generates (patch file_open), for any executable output files, patch its main entry point and add in a payload.
When a compromised compiler is generating your compiler, it will patch your compiler's entry point and add in an extra payload. When your compiler compiles another compiler, it will do the same thing, and so to any other programs it generates.
It's virus writing 101.
It's very easy to play "specialist" and come up with theoretical scenarios, like the idiots that think it's possible to attack git using SHA1 collisions
In the purely theoretical sense, RSA is also broken, since you "only" need to gather a lot of computers to factor a key.
If you are not willing to waste money on proving a point, why would you expect me to waste substantial effort to write code to prove my point to you?
And if you are not willing to put money behind your statement, your one-liner talking point is exactly what it says, "talk is cheap."
I at least put in the effort to build detail case to rebut the previous comment poster's point and showed how it can be done. If you think my point was wrong, build a detail case to rebut it. Then we can have a meaningful discussion; otherwise, it's just cheap empty talk.
BTW, what I talked about was not theoretical. That's how viruses are written. You don't have to believe me, but again it's not my job to convince everyone.