Experience is a deeply nontrivial topic and there are many very different philosophies how to handle it, including different attempts to do without, or concepts to have for example different sources of experience, different types of experience to improve your character in different ways, etc.
Experience remains a popular concept that is used in most games. So I dont know whats supposedly "dated" about this topic. Calling a very universal concept that everyone except a few outliers uses "dated" is just very strange.
The situation with experience is very much like the situation with hitpoints. There are obvious drawbacks to the concept, but on the other hand its amazingly simple, compared to more complicated solutions. Solutions which always have to answer the question if the additional effort results in actual gain in regards to gameplay quality. Of course in regards to hitpoints, there is for example Fallout, which replaced hitpoints with hitpoints per body part. Losing all hitpoints on your head or the torso (easier to hit than the head, but also has a lot more hitpoints) is just fatal, but if you lose your legs, that merely means the movement is impaired, and if you lose your arms, well then you are restricted in weapon use; however the later four variables can fall to zero without killing you. This basically changes a single variable to six variables, without complicating much further; a decent change that works pretty well overall.
The Elder Scrolls is an example for how to have a system without experience points, but still levels etc as usual. I cannot say I like the TES idea much. Since you level by using your skills, you get the strange situation that you literally cannot do certain actions because you dont want to level the related skill. And there are many more problems with this system. For example because running is also a skill in TES, you move quite slowly at the start of the game, while running quite quickly at the end of it. This is frankly really annoying.
A very pure "roleplaying" solution can be found in Vampire: The Masquerade: Bloodlines. In this game ONLY quests give you experience, and you use experience to level your skills. So there are no levels as such, you just improve your skills. Because the developer has very high control over where the player can go, this allows to know quite well what powerlevel the player at this point in the game will likely have, and allow to scale encounters pretty well to that powerlevel. All in all it doesnt work flawlessly, because newbies can easily screw up their character royally, making it impossible to manage certain hard encounters of the main story that you cannot avoid, but once you learned the ins and outs of the game, you can relatively easily navigate it. Though even with that I had problems to solve hard encounters on Nosferatu, the weakest of the clans.
Btw one could make the only XP for quests idea even more extreme by only rewarding quest xp for unavoidable MAIN story quests, while all side quests only give you item etc rewards. This way one would have full control over how powerful the character is.
But all in all I would be very surprised if we dont see just another example of classic experience with levels. Probably with different sources of experience, just like in BG3 (quest xp, dead opponent xp, protagonist xp and exploration xp). And very likely there will be again people who optimize this to the maximum.
That seems to be the most likely way this goes, and I'm frankly perfectly fine with that. Aside from pseudo-ideological arguments like "outdated", I dont think there is anything actually broken about this concept that needs fixing. Quite on the contrary, in my experience systems like that work best. You really have good control over how you want to develop your character, and the programmer can have a pretty good idea about the powerlevel of your character, allowing them to keep a good level of challenge - not too easy, but also not too hard - that is great to have to neither bore the player with overly easy encounters nor overly frustrate the player with impossible encounters.
