Whether LLMs are the right approach is a separate question.
In SQL optimization, the problem is a bit trickier (IMO) because compilation is in the query path. One successful approach I know of is Bao: https://arxiv.org/abs/2004.03814
Current compilers use a complex set of heuristics, a more holistic approach the kind neural networks do might outperform.
Additionally, there are other factors to consider when productionizing these systems. Compile time is important (which LLMs will almost certainly explode), and anyone concerned about code size will probably be doing (Thin)LTO which would require feeding a lot more context into a LLM making inlining decisions.
1. https://arxiv.org/abs/2101.04808 2. https://dl.acm.org/doi/10.1145/3503222.3507744
1. https://github.com/google/ml-compiler-opt/pull/109 2. https://youtu.be/0uUKDQyn1Z4?si=PHrx9RICJIiA3E6C