I tend to think of levels as being useful and entertaining tools that have nothing to do with realism.

In GURPS, if I remember correctly, you can gain a point in a skill through hundreds of hours of dedicated study or thousands of hours of just working using it. I have been in a campaign where this was the ONLY advancement allowed. Realistic, perhaps (sort of - I think I learn faster than that in real life!) but not very much fun.

D&D is based on the common fantasy trope that characters develop fast while Living an Adventuring Life, and I tend to be pretty happy with this - providing I am careful to make sure everyone's character gets a spot written just for their role, and give out XP for a pretty broad range of adventuring experiences not just slaughtering things. That goes quite a long way towards reducing some of the sillier effects of the XP system.