It's rather silly that we're punished for doing the Undaunted dailies because of how the Random Dungeon and Specific Dungeon queue appear to work; I get Random queue pops far faster than Specific queue pops. Which implies there's two separate pools.
Instead, why not treat it similar to these Writhing Wall event dailies. Where you pick up a singular quest to complete a dungeon of your choice (ie you can use the Random queue). That rewards a chest that gives you, say, 2 keys. Then there's follow up dailies that, again, task you with finishing any dungeon. But these reward a chest that gives only 1 key. Repeat these follow up quests for however many you wish players to be able to do per day.
This post comes after being in the queue for Graven Deep for over 2hrs, and not once has it popped.
PS: Since this involves a 'game system' (daily quests) I posted this here.
You have to learn the rules of the game. And then you have to play better than anyone else.