I've always hated XP. It seems that it only serves to take people out of the game mentality. It makes me feel like I am in a very slow video game.
It rewards what you want it to reward so instead of keeping up with a bunch of numbers to kill creatures or count money I would rather have them focus on playing their characters.
I could spend all of my time adjusting numbers of creatures to match a certain amount of XP per session to have them level at the rate I wish or I could write a story.
Putting it as "have them level at the rate I wish" makes it sound like the players don't have much choice in the matter.
Because, as an odd but significant side effect, using XP gives the players some choice in how fast they level or whether they level at all, in that they can choose to do things that earn more or less XP, or choose to cycle out a higher-level character and bring in a lower-level one (thus lowering the average level of the party), and so on.
The game has a sweet spot, regardless of edition (though it's at a slightly different level range for each); experienced players know this and may - for any variety of reasons - want to keep the game in that range.
You're also assuming they're going to get to all those creatures in that session.
It's simple and it means that when you choose to kill a monster then it is because you need to and not because you want to level. The choices are only for in game reasons.
This is valid, and speaks to a need for an XP system that is not so dependent on combat*. I'm hoping 5e somehow has an XP system that works equally well with all three pillars, though I'm not holding my breath.
* - 1e's XP-for-treasure was one such, but the treasure part was so high that if used as written they bumped every time they sneezed.
Lan-"I'd type more, but I have a date with some XP"-efan