Leveling up is just a game construct that allows a player to simply keep track of their character's progress. In the game world, the character is learning new things all the time, but the game is designed with only 20 levels in mind. 100 levels would make the progress from level to level more "realistic", but it would still be a game construct approximation. To reflect reality, you would need an infinite number of levels that encompass training, ability, regression of skills due to non-use, hourly/daily/monthly/yearly ebbs and flows of energy and potential, where the sun is in the sky, what the character has eaten/drunk lately, and myriad other factors that the D&D system just doesn't keep any tracking for.
In other words, D&D does not equal realism. Deal with it.