Well, yes and no. 4e went very much out of its way to provide non-combat xp awards. Spent a considerable amount of time on it in the DMG and whatnot.
The reason we don't have the 2e style one in 5e is because everyone is supposed to have the same XP. Additionally, in 2e, all classes advanced at different rates, so, the bonuses they got for doing their class stuff had greater or lesser effects. I remember that the clerics in the games I played in 2e gained the lions share of their xp from casting cure light wounds. 100xp every casting? Yes please.
The thing people tend to ignore in all this is that the game has become less and less combat focused over time. AD&D was pretty much all combat all the time. Why wouldn't you? Killing stuff netted treasure and that netted you xp. I've never understood this story that gets put out that AD&D wasn't about clear cutting the dungeon and stripping it down to the paint. Why would you ever leave a monster if you had the choice? 2e tried to become more about "story" but it was clumsily done and tended to lean very much on the heavy handedness of AD&D resulting in all sorts of problems. If your DM is "Always right!" then you can never complain about railroading and being sidelined.

3e spent some time trying to award xp for non-combat, but, it was mostly lip service and the adventures certainly didn't push in a non-violent direction. 4e was really the first honest attempt at trying to make a viable D&D game where you actually didn't have to kill anything. Heck, every single PC in 4e could, after something hit bloodied, end the fight with a single skill check. At least in 5e, you can declare that you're not killing something after you've done damage and put it down.