I like the campaign dungeon as the always-there default activity and occasional quest hub. It makes it a reliable resource to ensure a game can always happen. But there definitely needs to be tons of other stuff going on that the players can do if they want.
I have seen this used quite effectively, and it seems to be the default mode of play for the really early stuff (Blackmoor Castle Dungeon, Greyhawk, etc). The open campaign table-style of play (and the modern "Wilderlands-style" that formalizes some of this) helps there.
But the other thing that I have seen make this really work are NPC Adventurer Parties. I remember in one large dungeon we ran into a locked wooden door that some-one had modified a view-slot into. It was a party of elven mages and fighters who had been entering the dungeon once a month and had secured a "long rest room" that only they had they key for, about 3-4 turns (@ full speed not exlporation speed) into the first level - right nearby the 2nd level stairs. They were uber paranoid, as they had to re-clear the first level each time they cam back (evil cultists, and spontaneously generating goblinoids from "the black pits" were a feature of the dungeon). Our party worked out a deal with them to trade mapping information by leaving notes for each other, and we left a bag with 10 GP in the room in front of their camp-room as a show of good faith (they still never even opened the door while we were there). That type of stuff is GOLD for role-playing in the dungeon. I didn't get to continue that campaign, but I always wanted to find out what faction of elves they were with (gods were they paranoid) and make a more formal alliance against the goblins.
Or, and I almost pulled this complete arc off against some players while I GM'd Earthdawn: have a "rival" adventuring group that shows up every once in a while and competes for the adventure's treasure/goals/etc. Not enemies, just another party that has slightly different specialties, so maybe they get to the macguffin before the player do. Then, while the players are off following their own thread in the sandbox, have a rumor arrive that their rivals have been COMPLETELY wiped out while attempting to tackle the local megadungeon. If that doesn't set a hook to go back and re-explore that dungeon, then a week or so later, have one of the rival's come back as a form of undead and attack the player's party (trying to steal something specific, or kidnap some-one they have a link to, etc). Make sure the undead NPC is identified by others in the act. "Wait?! I thought she was DEAD?!?!"