No, it's like saying "a computer can't crack SHA hashes, it can only add and subtract numbers together" "a computer can crack any SHA hash" "yes, given infinite time".
The fact that you need infinite time for some of the stuff doesn't mean you can't do any of the stuff.
If it's executing a program, then the easiest way to make it more efficient, is to ditch the LLM and just execute the program. The LLM in this case is basically only (very very very very very inefficiently) approximating the very CPU it's running on. Just use the CPU to execute the program! And you won't be running it on an approximated processor, you'll be running it on a deterministic, reliable one that will not give the wrong answer ever (given the right program and correct input, of course, and assuming no hardware failures, which would affect LLMs too)
The fact that you need infinite time for some of the stuff doesn't mean you can't do any of the stuff.