I'm one of the devs. Our model is fully voice-to-voice, no text was involved in the making of hertz-dev for exactly this reason.
It's interesting to think about what complete diversity (i.e., no tendencies toward homogeneous conversation partners whatsoever among training data) would yield, given that it's trying to deliver whatever is most probable.
On the technical side having some sort of continuation or summarization loop on seems interesting to me as a product feature. It’s not enough to build a company off of though. But it would be nice.
If you use completely unprocessed speech data (including speech information with background music on YouTube), I think the potential will be higher, but the requirements on your computing power are too high. If you don’t have money to buy a GPU, just use voice noise reduction processing first.