Nope, there's absolutely no reason to level up, in fact quite a few people specifically avoid leveling up, and play the entire game at level 1 as you said. Unless you are efficient leveling (which is incredibly grindy and turns playing into a chore) then leveling up will only make you weaker relative to your enemies. God help you if choose to level up without combat skills.
Also, thank Bethesda for changing the leveling system for Skyrim, and removing (or at least greatly reducing) the level scaling for that game.
Also, thank Bethesda for changing the leveling system for Skyrim, and removing (or at least greatly reducing) the level scaling for that game.