"Deterministic" is not the the right constraint to introduce here. Plenty of software is non-deterministic (such as LLMs! But also, consensus protocols, request routing architecture, GPU kernels, etc) so why not compilers?
What a compiler needs is not determinism, but semantic closure. A system is semantically closed if the meanings of its outputs are fully defined within the system, correctness can be evaluated internally and errors are decidable. LLMs are semantically open. A semantically closed compiler will never output nonsense, even if its output is nondeterministic. But two runs of a (semantically closed) nondeterministic compiler may produce two correct programs, one being faster on one CPU and the other faster on another. Or such a compiler can be useful for enhancing security, e.g. programs behave identically, resist fingerprinting.
Nondeterminism simply means the compiler selects any element of an equivalence class. Semantic closure ensures the equivalence class is well‑defined.