Oh it's cute, let's not pretend that it isn't lol. But vestigial as hell. There was so much you could do with it, but it's just a crude compromise in the end and screams "we ran out of time" design-wise, to me anyway!
I mean, you're kind of getting at a point between RP and G here, which I don't everyone really thinks through.
No codification at all is essentially "pure" role-playing. No rules even. No DM/ref maybe. Just people telling a story together.
But that's not an RPG in any meaningful sense, that's just RP. We saw this a lot on the early internet - the clash of people who wanted to play RPGs online, and people who just wanted to RP, and didn't want the G.
Codification is essentially what the G is. All the rules are codification. There's no bright line between saying "this is how you make an attack role" or "this is how many actions you can have in turn", and "my ability Hawkwind Blade pushes you back 2 squares and does 2d8+STR damage" or "I fire 3 magic missiles each automatically hitting and doing 1d4+1 damage". That's all the same thing.
In a sense, your generalization is right in that, in pure RP, the "players" (who aren't quite players in the sense we'd mean), who have no codification to deal with, are totally free/empowered. But then you bring the snake into this garden of eden - the DM, the ref. Once you've put him in, you've privileged him over the players, and you've shifted power from the players, to him. They are disempowered by the codification that the DM is "in charge", and will determine whether their RP takes effect.
So that first codification, eating the apple if you will, is hugely disempowering, which aligns with what you're saying. All the power is taken from the players, and given to the DM. All of it, every ounce.
However after that, pretty much all codification, even DM-side rules,
ultimately shifts the balance back towards the players, because it limits what can happen, and the players can still request the DM to do things, but they also have other options, which he kind of has to agree with. A DM can't just say "Your magic missile doesn't work", without like actually engaging with the fiction and giving a reason why, for example. To do so would break the social contract between both parties, where without codification, it would not.
I think what the point of confusion some people have is that individual rules can be quite restrictive. But once you know they exist, you can work within their framework, and the DM is also restricted by them. 3E is a superb example of this. It's rules effectively massively restricted what martial players could do, relative to what they could do with a good-natured DM in 2E. But even for them, they could work within the rules and make more demands of the DM than they could in 2E. That's just not arguable, it's demonstrable fact. That's a unarguable power-shift the players. More codified abilities, even weak ones, for the players, means more actual
power for the players. Power. Let's be specific here. Power. It's bit like rights - yeah, if you have no written rights, you could be treated incredibly well. If you have pretty pathetic rights, you could extremely poorly OR extremely well, but the baseline is higher than with no rights at all. With no rights at all, you can be treated in any way - eventually the social contract is broken of course, and that's also true with RPGs, but history of the real-world and RPGs shows people can be pushed incredibly far before they actually snap and leave games and so on.
And older versions of D&D show this interesting double-standard where some PCs have a ton of rights, via being casters, and others have basically no rights beyond "the right to hit someone with a sword for 1d8 damage". If you look at 4E, at combat, the players are unarguably more empowered than, say, 3E, and there are two angles to this - first off every class is empowered in that they all have codified abilities, and can tell the DM what happens, rather than merely asking him, and rather than only some classes being able to do that. Second off, they still have the ability to request the DM to do stuff outside that - this was an interestingly frequent misconception re: 4E, the idea that you literally couldn't do anything not on your character sheet in combat. It's objectively and non-arguably false. 4E explicitly calls out that you can do this, that you can ask the DM, and even has optional and extremely numerically generous table that the DM can use to adjudicate how much damage your non-fixed actions might do and so on, or what effects they might have. This is why 4E is sort of regarded as a "wargame" in some ways - a type of game where both sides are equally empowered. Because in combat, that was basically the case. Outside combat, things were less-different to previous editions.
As for your point re: modern environments being more suited to older school stuff - yes absolutely agree, but it's kind of half the picture, because you're still looking at what is basically a "trust-fall" or "consensual BDSM"-type situation. Yeah there's much better advice/resources for everyone involved so things typically go better (I still laugh every time I see a guy going on about his "old-school" game and how he's a "fan of the PCs", not because that's wrong, but because it's so different to the common experience back in the day), but lack of codification still means there's a distinct double-standard, and if the DM falters at all in certain respects it will disproportionately impact the players on the wrong side of that double-standard.
Sorry for waffling on about this, I think it's pretty interesting.