I do not use them that often. They are there when needed, but only come up once in a while.
The DM may be trying to impose suspense on the group by making the threat greater and limiting the PCs with both exhaustion and a time crunch. You could rebel and take your breaks to overcome the exhaustion and heck with the time crunch. If you only have 24 hours before doomsday and you need to rest, then rest and let the DM figure it out. Not the most friendly way to game, but the DM may start to get the hint.
A less combative way is to hire lots of retainers. These extras can scout and guard and provide security while you sleep. Hire lots of people that guard and groom the horses as well as carry the torch and sets up camp and gather the wood. If you have 50 people waiting on you while you explore, life is easy. Kind of like in the old movies where there is a wagon train of locals waiting on the hero to find the lost city of gold.