I was just re-reading this. Although some have been hinting at levels being incompatible with a simulationist game, I've avoided thinking about eliminating levels, because I believe I read an article by Mearls that levels was one of the sacred cows of D&D (along with ability scores, etc.) that were essential to the game.
As we discussed, in 3E, levels primarily represent combat experience, and in 4E, they represent adventuring experience. Let's call it a heroic Combat Level and an Adventuring Level, respectively.
One thing I didn't like about 3E NPC rules was that it was applying Combat Levels (with attack bonuses, hp, etc.) to a non-combatant. Really, the level should be indicative of their life experience. A blacksmith should have a Blacksmith Level where 1 is apprentice and 5 is Master and you get x skill points per level and maybe a Str bonus. That's just a theoretical example, I'm not advocating actual Blacksmith Levels except maybe in a complicated game (although using that as a general guideline for NPC creation might be useful, I'm not sure).
Some questions - if a scrawny rogue is hanging back at every battle and allowing everyone else to do all the fighting, does he get xp towards a Combat Level? If a fat scholary wizard never helps anybody around the dungeon and keeps a nose buried in his book, does he get xp towards an Adventuring Level? If the game is sandboxy, is it justified to eliminate scrawny rogues and fat scholarly wizards from the game, or do you allow them as viable characters? If the latter, does the player want to receive a Combat Level or Adventuring Level and why?
All this musing is to suggest to me that a truly sandboxy Lore edition might be quite different than the Legends edition, not just by toggling of core rules, but by toggling the quality of levels as well...
First, I'm not sure that you are using the same definition of "sandbox" that pemerton and I are using (or even that pemerton and I are 100% in sync, either). So maybe we'd better clear that up. For me, a pure sandbox is one in which there are defined limits (scope of the world, character power levels, what magic and can't do, and any number of such things, though not all of them in any given world necessarily)--that is, the "box". Then you have the elements that are in the box (mainly, characters, NPCs, monsters, locations, items)--that is, the "sand". The characters go an interact with those other elements inside the box, and the DM referees.
For a pure sandbox, there is no preplotted action whatsoever. (The DM may have notes about goals and motivations, and things NPCs will do if not interfered with, but as a purist referee, these are are tentative.) More commonly, you'll get a less pure version where some of those major events are allowed to roll along (albeit somewhat modified if the players interfere) in order to keep the action moving. (I have seldom run a pure version, but I've come fairly close a few times.)
That says nothing about styles. I've run almost pure hack and slash sandbox. I've run a mostly purist simulation exploration sandbox. I've run character-based exploration with the sandbox as background. And right now, I'm running a strange cross between a narrative, character-focused sandbox and a straight gamist, dungeon crawl sandbox. If internet reports can be trusted, there are a few other possibly sandbox styles, too.
Your reservations about levels are one of the classic responses from someone who wants D&D as pretend simulation. (For clarity, there is no judgment being made here about that style, though I don't favor it personally. If the "pretend" adjective is too much, I'm open to another.) It is in contrast to someone like me or pemerton, who when we play simulation, want to move to a game that overtly supports that style, like Runequest. I like rules with a clear style in the mechanics, even though I often like games to be played in a muddle. It is easier for me to drift from a known point. Apparently, a lot of people like games with a muddled style in the mechanics, which they can then tweak this or that to get where they want.
So yes, one of the ways to make the pretend simulation crowd happy is to remove some of the power from levels, but keep the heart of adventuring in levels. If they wanted the
adventuring removed from the levels, then they would be one of those first two groups I mentioned earlier that play D&D but don't like it being D&D.

But you can take out a certain amount of the peripheral stuff and still make something that is recognizable as D&D. There is, for example, no
inherent reason why skills or ability scores need to scale with class level. If they don't, many things that the pretend simulation crowd wants will be easy to achieve (e.g. wizards with no particular ability towards opening doors).
However, let's not go to far and assume that you can stop there. Pretend simulation may be a sizable portion of D&D, but it is not all of it, and I doubt even a majority. So whatever means are chosen, there had better also be a way to support people who want their wizards broadly competent by the time they are 10th level wizards--and it had better work mechanically, too (unlock 3E skill ranks, in this respect). A narrowing of the scaling of DCs is the most obvious way to satisfy both groups, and I doubt a better one (i.e. one with less nasty side effects) can be discovered.