You can do a lot of dungeons with 4 DPS already. I once did Castrum Meridianum and Praetorium each with 8 DPS and we were successful. Ultima was challenging but we found a way to beat it the second time.

What you learn about removing either tanks or healers is that the game becomes a lot more fun. I would want to remove tanks, personally, because then enemies would run all over the place like Rathalos.