Actually, yes. I most assuredly can frame it such that levels are not, in fact, rewards. When you go the route of ignoring XP rewards, and go for alternative rewards, levels quite explicitly become nothing more or less than a metric of the relative power level of the PCs compared to the rest of the campaign world.
However, and to me just about as important, levels are also a measure (one of many) of the PCs compared to each other.
You are removing rewarding players with XP from the equation entirely, hence you are by definition removing leveling up as a reward entirely. Levels become a metric, not a reward; there's a significant difference.
But when they're a metric comparing PCs they also become a reward...again, one of many as you so well point out...
Instead rewards are, in my campaigns at least (as I posted previously in the thread), much more tangible in terms of their impact and immersion within the game world itself.
You don't get to have a castle in the game world unless you earn it.
You don't get titles unless you earn them.
You don't get to command an army.
You won't have as many magic items (yes, you'll get a baseline of wealth with which you can purchase items, but that's it).
You won't have as many spells in your spellbook, if you are a wizard.
You won't have any favors with powerful NPCs.
You won't have a license to kill (in the literal sense) in this country.
...here.
But your level? Your raw mechanical baseline? Yeah, you're all on even footing there, because it's been entirely removed from the reward structure. Rather than worrying about what can often be a complicated balancing act of rewarding XP for killing things in combat versus fair rewards for characters who simply don't engage in nearly as much combat, you run under the baseline assumption that everyone in the campaign is engaging in activities they are gaining experience from, maturing because of.
However, whether combat or not I want to recognize the characters who participate rather than stand back or stay at the inn. That's where xp come in.
You don't worry about rewarding XP for good diplomacy, instead someone gets a favor, a title, a trusted contact in some organization.
You don't worry about rewarding XP for successfully breaking into an evil wizard's tower without getting caught, you actually gain a tangible, physical reward no one else in the party gets, because they didn't join you in taking the risk.
You don't worry about rewarding XP in combat being by far the most common time to gain XP. Each combat will have its own rewards, or sometimes (and I know this is likely to make some shudder), a given fight will have no rewards at all. Engaging the random 1d4 griffons that happen to commonly be in the area not only didn't give you any rewards for killing animals that are part of the natural order, if you persist in such activities too much you might upset the natural order. The people that just killed a pack of alpha predators, rather than just scaring them off, likely did more damage than they might think to the local ecology. The local druid might not be too happy about that.
All good, but nothing at all says xp can't go on top of all that. The characters involved in the diplomacy get xp for it; the ones who rifled the wizard's tower get xp for that, and those who helped knock down the griffins get xp for that. This allows for a greater reward for a character that was involved with all three activities than in just one, or none.
Side note regarding your wizard's tower example: in our games its a long-standing player-driven tradition that all treasure and booty is divided equally, meaning it's quite rare that a DM can use acquired treasure as a reward mechanism like you suggest here.
So yeah. Actually I can and do remove XP, and leveling, from the reward structure entirely. Levels are a yardstick measuring where the campaign currently is, and the PCs, even new PCs, are movers and shakers within the campaign world at that level.
So what do you do with all the things that can change an individual character's level on the fly? For example: I have level-draining undead in my game. Decks of many things and the like can give or remove a pile of xp on the spot. Wish spells, rare though they may be, can give or take levels if done right.
Also, how do you handle characters who die, stay dead for an adventure, then come back? Do they get equal xp or levels for being dead? (if yes, this seems kind of ludicrous)
This doesn't mean I don't understand the other approaches, and I am fine playing in games that use them. But ES@1 in particular is running under a particularly bizarre assumption: That only adventuring in an adventuring party can truly help you climb past 1st level.
One can assume that anyone else in the game world who is above 1st level is already busy doing other things...
That said, I don't subscribe to full-on ES@1; but I do insist that new or replacement characters* come in either a level or two below the party average, or a level below the lowest, or at a floor level, depending on the campaign. There's lots of other levelled entities in the game world and lots of ways to gain levels other than adventuring; adventuring just happens to be by far the fastest way. But when Kallie the Thief dies and the party go looking for a replacement it's almost certain the replacement will be lower level than Kallie was.
* - unless it is a player's FIRST character in that campaign, in which case it comes in at the party average.
Having every new PC come in as a novice, just starting out in the world for the first time, effectively eliminates a huge number of potential backgrounds for why someone would be joining your high-level group of adventurers. Drizzt is joining up with your party of 11th level characters on a dire mission to save the North? Well, he's just a 1st level ranger, fresh from Menzoberranzan. Raistlin is joining your party, having already earned his red robes, and the title Wizard of High Sorcery? He's 1st level, even though the rest of the group is 15th level and in the midst of a massive campaign against armies of evil dragonriders...because.
It just ends up causing a pretty significant disconnect, because young, inexperienced characters wouldn't likely be WELCOMED into a seasoned party. Not unless they are extraordinary, and even those would be the exception that prove the rule. One? Maybe two such characters coming in at so low a level in a mid-to-high level campaign? Sure, ok, perhaps. But all of them? Not without eliminating an enormous percentage of potential back stories, or making those backstories not mesh with the relative power level of the character itself. Sure, your druid has been protecting these lands for decades, but she only knows a handful of the weakest of spells in a druid's repertoire, deal with it. That...is a bit too draconian, too heavy-handed a rule to impose, imho.
Yes, I agree there's holes with strict ES@1 which is why I don't do it; though with that said it's trivially easy to dream up a logical in-game rationale for it if desired, which might go:
The only true free-agent adventurers are those fresh out of their 1st-level training. To adventure in the field, these characters must first sign on to an Adventuring Company (of which the PCs-as-a-whole are one), and once signed their allegiance may never change on pain of death; this is strictly enforced by the Companies themselves to prevent recruiting wars, defections, and what the modern business world calls headhunting. Thus all experienced adventurers are signed to a Company, and if your Company finds itself shorthanded its only recourse is to recruit raw 1st-level free agents. For taxation purposes, the King's agents are constantly kept advised of the membership of each Company.
To think that up took as long as it did to type it; it's not perfect, but more thought might give better ideas.
Lan-"if you ever get a 1st-level version of Drizz't in your party, do us all a favour and kill it immediately"-efan