I think the simplest 'fix' would be to allow lower level classes to turn in daily beast tribe quests similar to how lenient the Ixali beast tribe quests are for crafting classes. I always though it was a bit silly that you can't turn these quests in until you're nearly done leveling a class anyway.

If they added new low level dungeons they'd only make ques longer. It would just dilute the options people have currently. It wouldn't make players who aren't currently doing low level dungeons suddenly start doing them (except perhaps once for the initial clear).