once you are done with the final chalice boss you can remove the chalice, no need to run them again unless you wanted to farm trash.
there are public keys (passwords) for some chalices posted on reddit/neogaf/etc that have specific loot drops, like a ithyl that drops a better burial blade and a blood rock, etc. you need to create the root version of that chalice and then type the password to spawn that specific set of mobs/loot, so might be useful to keep some of the later chalices around for that.