From a scientific explanatory perspective, the old models are not obsolete because they are explanatory whereas LLMs do not explain anything about human linguistic behaviour.

On one hand you have models which you argue are explanatory, but arguably do not work.

On the other hand, you have models that not only work but took the world by storm, and may or may not be made explanatory.

You either invest more work getting one explanatory model to work, or invest more work getting a working model to become explanatory.

What do you think is the fruitful research path?

What do you mean "work"? Their goal is not to be some general purpose AI. (To be clear I'm talking narrowly about computational linguistics, not old fashioned NLP more broadly).