I don't know if not talking to the companion has consequences later on. However, what you propose I could see it help me remember to visit the companion room.
I like the idea of the companion suggesting or hinting at their need to talk with the protagonist once every milestone reached.
I'm leaving this small suggestion that came to my mind right now:
Each time the protagonist moves between floors, the system could check for the requirements needed to have a chat with the companion and would warn us once, every time they reach a certain milestone.
I hope this helps in getting an idea.