GP did say 'reimplement' (not making it sound trivial, like 'add a sqlite backend plugin') in fairness - i.e. in your terms 'why not implement the ES API for sqlite'.
More like "make a thing that's a bit like elasticsearch, but exposing sqlite query language to a sharded event store" -- not "make elasticsearch but use lucene" because elasticsearch is lucene, and reimplementing it via sqlite wouldn't give elasticsearch.
I'd call it elasticite and then (correctly!) be sued by both elastic and the sqlite orgs...
