I agree with you on every step and every point except the LM. Your entire argument hinges on FTS requiring a fat RDBMS. This is not the case.
Postgres is what I have experience with, but I just looked up SQLite and indeed it has FTS5[1]. This is not an LM-grade problem, this is a solved problem.
It's why Kiwix was developed, so people don't have to run a full web stack (which requires a rdbms) for wikipedia.
I don't know if LM is the answer and probably not in power deprived areas, but running a rdbms is defintely isn't it.