In my experience these types of situations only come about through ignorance. This is anecdotal so YMMV but most people I've worked with who propose Mongo don't know SQL and don't generally want to take the time to learn it.
Quite often they will have also read somewhere that joins are slow and have managed to convince themselves that the solution is to avoid relational databases altogether. Or maybe that's just how they justify it.
Seems to me that it’s on your devs to explain to the business why their poor technical choices now necessitate a substantial additional investment to get a usable solution. When they could have just used Postgres, and they knew it.