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."
Not only that, there are items, spells, and monster effects that render a player exhausted without the DM's say-so.
