FrogReaver
The most respectful and polite poster ever
Actually, I feel pretty strongly that XP for fighting is the way that makes the most sense. Not that it's perfect, but I feel like it makes more sense than most of the alternatives, especially in 5E. The only real problem with it is that spellcasting also progresses through combat, and you'd think that spellcasting would be a broad enough ability that you don't need to fight in order to improve it - there should be some order of pacifist wizards out there, and they shouldn't be stuck at first level forever - but then I remember that the rules are only really meant to describe professional adventurers. Presumably, non-adventuring wizards can progress through study and practice, in the same way that NPC carpenters can improve their skills.
I could rationalize milestone levelling as something that makes sense within the world - that your abilities advance when the DM believes you have accomplished enough to have actually learned something - but I would rather not. In my experience, it doesn't make for fun or exciting gameplay. Fifth edition has already removed all of the danger from combat, since you regenerate completely overnight, so getting rid of the XP would make combat a huge waste of time. If combat isn't tense because it's dangerous, and it's not exciting because you get nothing out of it, then there's no reason to care about it at all. It becomes perfunctory, going through the motions because you feel obligated to, rather than because it's actually fun.
Doesn't leveling represent your character getting better at everything? Not just at combat? If so then why is combat the only thing that levels you? Even fighters and barbarians?