More good insight on XPs and how people see them.
I'll note, firstly, that I do not advocate complete removal of XPs in 5E. I'm just saying, don't push them as the default assumption. For those that want to use them, a simple system could be contemplated, for example:
XP = monster level X 100 X (monster type)
where monster type = 1 for normal monsters, 2 for elite, 4 for solo, etc...
Or, you could even have XPs in the monster manual. But propose to groups to use a more simple system, and those that want to continue using XPs for all the good reasons mentioned in this thread, can do so.
Why remove them as the default assumption? Well at least to cut down on the XP calculations by the DM as he prepares adventures; by the DM when he needs to distribute XPs; and by the players when they receive XP.
Many posters mention that it's easier to ignore than it is to put back in. Not sure about that. If XPs are either easy to calculate or even provided in the monster entry, then it's a breeze to bring them back in. However, by not having them as the default assumption, you're saving a lot of groups, a bit of time every session, every game.
Presently, my impression is that XPs are being used at least in part because they are not being questioned. In AD&D (and in old-school type games generally), they made more sense because it was frequent to have characters evolve at different rates, each class had varying XP tables, PCs might encounter monsters of way different level than theirs, and so on. But now? Since 3E, things have changed. Now, in 5E, classes have a single XP table, commercial adventures are designed expecting PCs to be of a given level as I mentioned. 5E appears to have the 4E approach, and therein the XPs had little use, really, if commercial adventures were run, or if your adventures were like commercial adventures.
I'll also throw another fish in the bucket. Removing XPs might very well help immersion and the pleasure of gaming. (I can hear the "oh's!" and "ah's!" from here

.) I've played AD&D for 15 years, a while back, and got back with my old gaming group a few years ago in 4E, after having played with other people for the last decade. My old gaming group had used XPs, while my newer group had ditched the XPs a while ago (we initially used them too). The first fight in my recent game with my old gaming group was one where there ended up being a lot of tension, the party almost got wiped out, but they managed to survive, a great fight all around. When they managed to win it in the end, relief, smiles all around, players playing in-character and talking about trying to figure X-Y-Z about the opponents, already getting into the plot... And then one player asks: "so, how many XPs do we get for this?" And all players forget all about the story and the fight, and they all happily pick up their PC sheet and their pencils, and go "yeah, how many?"
This kind of broke that moment for me. It was like, out of the story, and into the meta, to calculate XPs. Boy was that a bummer.
Now I know many groups give XPs on a per-session basis, instead of per-fight; but that point remains valid, if less disturbing. XP is metagaming and is about giving rewards for in-game accomplishments. I find that that kind of reward is not required for the game to be fun; and on the contrary, in my personal experience, and according to my personal opinion, it is detrimental to the pleasure of gaming. It's like giving your son 25 cents each time he scores a goal when playing soccer, or one dollar when he wins a game of Monopoly against you. As humans, it's very difficult to dissociate the hope for the reward from the play experience (I know I can't). Pavlovian reflex? Don't know, I'm no psychologist.
Can't we just play without that reward?