Which certainly seems another step removed from logic.
The primary purpose of the leveling system in Borderlands, at least to my eyes, is to make it so you can't just pick up a gun on level one and use it the whole game, defeating the purpose of the main game loop to be forcing you to be constantly changing guns. OK, I get that purpose and in context it makes sense. But the leveling system is a really weird way to do it. I'd almost rather see guns decay instead. (Not do the whole "100% functional until they instantly and totally break"; we've got enough experiences with that to know how frustrating it is.) Decay is somewhat plausible though then you have to have the strength of will to reject repair mechanisms, which is still physically weird.
But I'm not really trying to propose all the solutions to all possible alternatives to leveling systems; I'm just saying "hey let's make the player and all the enemies 11% stronger every 30 minutes, except across a large set of dimensions impossible to ever keep scaled properly relative to each other in an exponential regime" is a silly thing.
I don't think the solution is just to rip them out and then proceed forward. And there are still other bad designs, of course; a sibling comment cites Oblivion. (Although I would call that an example of one of the "gyrations" I refer to; having a leveling system but then trying to remove it by somehow mathematically cancelling it is just weird. Quite distinct from not starting with one in the first place.)
I would cite something like Bayonetta as a good example of what I mean, though by no means the only possibility. Especially as "RPGs" continue to move more and more in the direction of straight-up-action-game combat anyhow. You open up some weapons. You can double your health and the other resource (forget what it's called), and I'm not even sure I love that, but you can. But fights are not about whether you're level 34 and they're level 63. Difficult fights are difficult because they are difficult.
In some sense the biggest mistake in my mind is that it gives designers such an easy answer; just slap a leveling system on it. More thought would be nice.
I could also cite something like Slay the Spire. No "levels" in sight, but your character certainly becomes more powerful over time, and your play gets better. Skill acquisition, clever combinations of abilities and features, etc. So much better than just a number that goes up.