So why are they so rare? It is expensive in several dimensions to build a narrowly tailored database engine from scratch. Database engines are not modular, you can't assemble them from arbitrary parts while maintaining control of their basic characteristics. Building an optimized domain-specific database from scratch is not trivial because you will have to do a lot of the really hard parts yourself.
In my head, there has always been a missing piece of software - a "database compiler", that can take the very complex and high-dimensionality abstract specification for a domain and codegen a purpose-built database engine. I also recognize that this is exceedingly non-trivial; I codegen storage engines to spec and that is already difficult enough. Doing that for a full database engine in a specific domain would have hundreds of input parameters, many of which would require expertise in the underlying codegen to know how to use them. It would be awesome if such a thing existed though.