The LSP is limited in scope and doesn't provide access to things like the AST (which can vary by language). If you want to navigate by symbols, that can be done. If you want to know whether a given import is valid, to verify LLM output, that's not possible.

Similarly, you can't use the LSP to determine all valid in-scope objects for an assignment. You can get a hierarchy of symbol information from some servers, allowing selection of particular lexical scopes within the file, but you'll need to perform type analysis yourself to determine which of the available variables could make for a reasonable completion. That type analysis is also a bit tricky because you'll likely need a lot of information about the type hierarchy at that lexical scope-- something you can't get from the LSP.

It might be feasible to edit an open source LSP implementation for your target language to expose the extra information you'd want, but they're relatively heavy pieces of software and, of course, they don't exist for all languages. Compared to the development cost of "just" using embeddings-- it's pretty clear why teams choose embeddings.

Also, if you assume that the performance improvements we've seen in embeddings for retrieval will continue, it makes less sense to invest weeks of time on something that would otherwise improve passively with time.