Combat itself is a core piece of d&d and there are no RAW rules that give exhaustion by simply fighting.
There may still be monsters whose abilities can give you exhaustion levels.
Additionally, the fact that most combat spells/abilities end after 1 minute suggests an inherent need for resource expenditure for longer combats.
Most combats generally resolve in less than one minute and for a combat to extend for minutes (never mind hours) would be extremely long to manage at the table.
D&D 5e is built around it's combat system that is meant to create these epic and heroic fights for the players. Realism has taken a backseat to simplicity and the goal is for the players to enjoy their experience. While there are RPGs that are realistic, difficult, and have systems in place to make combat much more difficult, 5e is not that RPG. The lack of combat exhaustion is a feature, not a bug for 5e.