It would be nice if we had a mathematics-wide push for formal verification of proofs, not just done by the mathematicians who really like formal verification. Maybe there could be a journal of only formally-verfified results?
I don’t think such journals can be the full solution, though.
Problem is that to entice mathematicians who don’t like formal verification to publish in it.
Conversely, there are many ways to do computer-formalization of mathematics, without every doing anything with HoTT.