Yes, it is a significant distinction. By fixating on this division you make your contributions irrelevant to overwhelming majority of people who play RPGs. The games where the players have significant mechanically-backed, narrative-level agency are fringe. And yes, pointing out that such games exist is fine, but but if you considering anything besides the players having mechanical narrative meta control not worth discussing, then we really have nothing to discuss regarding agency and you have nothing to discuss with most people playing RPGs. Because most games do not have such mechanics and they're not gonna.
Yeah, and I was being accused of being elitist up thread! ROFL! IME, of 35 years of GMing RPGs, a LOT of players are both eager for more than your formula, but a lot of them are utterly ignorant that it can even exist, so don't know to ask for it. In the REAL world the vast majority of people don't even know any RPG exists except D&D. This is not because they wouldn't be interested in, or maybe even happier playing, some other game. It is simply that D&D itself is a niche thing, and other games are niches of niches (how many people know about subgenres of Manga for example, and Manga is an industry that is 10x the size of RPGs).
Again, in my extensive experience, players EAT UP games that give them narrative tools and authority. This is especially true of people who are new to play, and particularly young people. Older people who have less energy to devote to games and/or have been trained on 'traditional' D&D (either 2e+ 'story teller' or 1e- 'Gygax Style') are a little trickier, they often need a bit of coaching to 'get it' or maybe just don't have the mental bandwidth to spend on doing a lot of agenda setting. It is fine to say that conventional D&D is good for them, I'm not into imposing things, but it doesn't follow IMHO that this makes narratively focused games less desired or popular.
And I think that by fixating on this one aspect, you ignore other aspects of how agency manifests, which are at least as important and are actually relevant to most games being played. Agency works pretty damn differently in a railroady adventure path, a narrative driven game where the GM improvises the narrative based on character actions and in a sandbox and those are the sort of differences that actually matter to most people.
Again, if you don't have agency to declare character actions, it isn't an RPG. What you are describing is 'illusionism' or 'force'. That is a 'railroady adventure path' is a game where the players are just an audience basically, reduced to merely rolling dice when prompted. This is hardly even role playing, though I guess it can be classified as a 'game' in some sense (Chutes and Ladders is generally classified as a game too). In the 'GM improvises the narrative based on character actions' then you are playing basically how we play, just informally!
This is art vs engineering thing. You're an engineer, I am an artist. And neither is right or wrong. But I don't want my creative processes limited or defined by codified rules, they hinder me more than help. You obviously feel differently.
I'm a fairly creative guy. Well, I like to exercise my (admittedly pedestrian) creativity. I don't know if 'engineering' informs my desire for structure in narrative roles. I think a big reason for it is simply because I am better with social interactions which are gated by formalisms. When the rules/process incorporates something, then I am sure to do it, and it happens smoothly. If its informal, then I'm left wondering if I did what I was setting out to do or not. Some people have talked about these mechanics distracting or restricting them, but FOR ME at least they make things much smoother and more automatic! I'm sure I could run a BitD campaign and it would mostly 'just work', but if I tried to do the same game using a 'classic' type of strict role set of rules, it would be MUCH harder to produce the same atmosphere and sort of play/narrative. Impossible really.