Bacon Bits
Legend
Why are they just 'exploring' and doing whatever they want?
No, but they must have some in game reason to hang out together, and delve into dungeons and fight monsters. One probably studied wizardry, and has a master/ fellow apprentices out there somewhere, and other is a member of an organised church heirarchy. These people have things going on in their lives. Friends. Family. Obligations. A reason why they are exploring. People to answer to.
Unless the campaign is a homeless, faceless, friendless, orphan with no connections to anyone or anything somehow finding reason to band up with four more homeless, faceless, friendless, orphans and spontaneously all deciding to explore the world for no good reason, Im sure you can come up with some kind of time limiting factor.
And if you cant, then use the longer rest variant.
Why don't you ask the PCs why they adventure. It very well may be to simply seek their fortune and adventure. To satisfy wanderlust, loot ancient tombs, defeat mighty beasts, and destroy the foes of the good and just nations. To earn enough renown to be granted lands and your own title. There are countless examples of people in our world just taking off and seeking adventure and fortune. Same story for why they're together: make the PCs come up with it.
Why is it up to the DM to tell the players why they're motivated to adventure? The DM builds the world. It's up to the players to decide their place. It's *their job* to adventure.
Seriously, has no one played an old school sandbox campaign?! Just wander around the wilderness, meeting new friends and foes, finding danger and adventure around every corner? You know, actually adventure. Didn't anyone ever have a campaign where the DM told them, "Just show up with a character, a reason to be adventuring, and a reason to be with these other knuckleheads"? You start the campaign in a tavern of a small town in BFE Greyhawk, and you hear rumors of bandits to the south, tales of a green dragon living in the forests to the northeast that's been terrorizing the town, legends of a lost tomb in the swamp to the east, whispers of a cult and missing farmers to the north, hints that the old wise cleric of the local church just isn't who he claims to be, and a merchant desperately seeking replacement guards for his wagons that will be leaving town in a fortnight.