Exhaustion is not only a BG1 and BG2 mechanic, it's part of D&D, and Larian is committed to being as close to 5e D&D as possible. IMO, if you're playing a Role Playing Game, you should expect a level of resource management. Would it make sense if characters were able to fight and fight for days on end without sleep? No.
The longer you go without sleep, the more exhausted you become. At first your skill-checks suffer, then your combat ability. Go too long without sleep and you die. It's not an arbitrary condition. It's meant to provide a sense of verisimilitude (realism).
If you are forcing your players to go without sleep, it is a setup you choose as a GM. And the debuff you get from it should be considered in any encounter you set up after that.
There is absolutely no reason for players to get exhausted in a session other than the GM decides that they will be.
Who is forcing the players to go without sleep? The idea of player agency is that they decide when to sleep. They decide when it's a good idea to rest; and they decide if they want to push their bodies to the limit. If a player character wants to try and scale a mountain I will let them...if they don't roll good enough Athletics, they suffer exhaustion (or fall depending on the scenario).
Exhaustion is a D&D mechanic. It's not designed to be a punishment the DM inflicts on players, but rather a consequence to a player's own actions. "You want to try to catch up to the horde of villains by traveling through the night without sleep? Ok, but you risk exhaustion."
It's not the DM's responsibility to take a player character's exhaustion into account. If they risked exhaustion and became exhausted, that's just the way it is and they have to find a creative way around it.
Not only that, there are items, spells, and monster effects that render a player exhausted without the DM's say-so.
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.
So, it is always the GMs choice what he puts on players.
(There are a few systems where this is not true, but none have anything to do with DnD)
Edit: Sorry missed the last part of your post. Well yes, there are effects that will make you exhausted. Those play very well into crpgs actually, and I think these are ok. I am not against the mechanics of exhaust at all actually, I just find it unnecessary in a crpg and kind of a waste of time in most TT games *shrug*
