I think it would be very difficult to completely beat SQLite with a Python library. My goal wasn't to beat it but to have performance that's within an order of magnitude which I think I've achieved.
In my opinion, the MongoDB interface has a lot of advantages over SQL that make sense in a lot of use cases. Certainly, there are times when a traditional relational database is the right choice. But I do think Mongita fills a niche.
Separately, the JSON1 extension, which the top-level comment refers to, is nice technically but has a challenging interface IMHO https://www.sqlite.org/json1.html