It is the GM that makes the story.
If the GM tells the players "You want to try to catch up to the horde of villains by traveling through the night without sleep? Ok, but you risk exhaustion." that is entirely up to the GM. It is his story.
What is he going to do if the players say "Nah, we sleep"? Let the story die?
All choices in any game are completely arbitrary. They are completely up to the GM. The GM is not forced to do put anything on his players that she doesn't want to happen.
I must say, if this is your view of the GM/player relationship, then you have played with some very horrid GMs.
@Gmazca is correct, the purpose of the game mechanics are to allow player choice. The GM referees those choices, and tells the story as the players play it, if the players choose to go after a horde of villains, that is their choice. If they choose to chase so long that they risk fatigue, that is their choice. The point of the rules is to explain the consequences of choice.
It have nothing to do with horrible.
It is a fact that the one that set up the choice to begin with is the GM. It doesn't just spring up out of nowhere.
Who else would have set up the choice? (Have you ever been a GM btw?)
I find this very insulting. Have YOU ever been a GM before? Or even a player for that matter? The GM sets up plot hooks, not the entire story. Sometimes our group simply ignores the GM plot hooks because we're really not interested. In some cases we come to blows when the GM doesn't expect it and in other cases it's vice versa.
The choice springs up out of what the NPCs the GM creates want to do, how the players react to whatever it is they're doing. If your entire plot hook is "There are goblins in that cave to the west, go kill them" and the players go "we wanna go south instead" followed by yours "you can only go to the cave" then I'm sorry to say, you're a HORRIBLE GM.
The issue comes down to where the line is for separate options. You're not exactly playing "Core Rules" without the exhaustion mechanic in place. You are tipping the balance of difficulty because you can perform any actions you want for as long as you want without the threat of exhaustion.
If exhaustion is toggleable in any difficulty, what other mechanics would be able to be switched on and off? Idk, but in BG2, if I used the haste spell twice before resting I became exhausted. That's just the way D&D rules work.
Don't worry, by the looks of things now, BG 3 will have so little to do with D&D core mechanics that it won't matter anyway. I say we also remove spells slots and make fighters hit like a truck for balance reasons and call it a day at this rate