Correct the Massindexer would need some new configuration options.
A fetch profile would be useful for the second phase, but an easy improvement I was having in mind is to have the first phase - which currently just loads the stream of IDs - to use a custom named query, so people could use a "join fetch" in their query if they want to.

That would only need you to declare the namedquery, and to specify its name on the MassIndexer - with the small API complexity that it can run for multiple types, so you need to specify for which type it should be using the specific named query.