EzekielRaiden
Follower of the Way
Perhaps, then, it might be useful to try to put some meaty steak on this salad?Just looked at the OP and just realized that if you think the definitions above are just "word salad" you are likely going to have a hard time understanding the issue. I think your in a car that can't turn left, you may want to go in for tune up.

@bloodtide
I said before, players want to feel responsible for their actions and the consequences that follow. Railroading, visible or not, harms that connection. Going on Space Mountain doesn't make you feel responsible for what you see. You decide, what, the outfit you wore? But anything that could actually change the track or ride is just impossible. If the destination is fixed, and the path to get there is pretty much fixed, it can feel like you are merely being told what to do. Sometimes, that's okay, it's what you want. But these players said that isn't what they want right now. Not a roller coaster; they want a jungle gym, or a box full of legos, or something like that. Scrape a knee, or have your tower fall over? That's on you, not something you just have to tolerate.
Such players, in those situations, feel they could really change the outcome if they choose differently. A weak form of agency would let players pick which bits of track to see on Space Mountain. They still can't control what track options there are, but at least they can control which ones they see, and (perhaps) what order. That's pretty low on the agency spectrum, but not nothing. Being "guided" toward certain choices is gonna be similar.
Lots of stuff with "agency" mentions "informed decisions." That's because it doesn't feel like you're responsible for the consequences if you made a choice because you were misled or deceived. Legally, this is a real defense: you can't commit perjury if you truly thought what you were saying was fact. Hence, if you want to feel like you have agency, part of that is usually needing to feel you had enough info to really choose.
If a player feels their choices don't do anything meaningful, or that they really couldn't choose for some reason (not enough information, being coerced, being forced to do only one thing even though other solutions also make sense), then they generally won't feel that they have meaningful agency in a game. If the destination is fixed, and the path to get there is pretty much fixed, what exactly were you doing when you participated?
Now, a big point here is, as you've probably noticed, I used the word "feel" at least a dozen times here. That's because, technically speaking, the feeling matters more than the actual fact. But this "technically speaking" comes with a huge caveat: If the players ever feel they were deceived about having agency, if they ever discover that you pretended to respect their choices, that all this stuff was merely an illusion, they will usually get VERY upset. We're talking "this can easily end games" upset. Because, while folks who desire agency might be annoyed or frustrated if presented with a game that they know doesn't actually give them agency....they'll feel betrayed and lied to if they ever realize that they didn't have agency but were led to think they did.
A player that feels the GM has lied to them won't trust what that GM tells them, and it is extremely hard to win that trust back. They'll second-guess everything you do, and steel themselves for another (perceived) betrayal, another (perceived) deception, which will make them much less likely to engage and participate, and much more likely to act out or criticize. This, for me, is the big reason why I don't--ever--engage in "illusionism" or "invisible railroads" or the like. I can fool smart people for a little while, but not for a long time. You have to fool your players indefinitely if you want to use these approaches, and I just don't believe that that is sustainable long-term.
Instead...the best way to make your players feel like they have agency--because they know enough to make choices, and those choices really do change the direction of the story and even the events that happen, and when they did so they weren't made to do it--is to actually give them those things. The best way to make someone feel that something is true is to make that thing actually true.
It would seem to me that the burden of proof should be on you to first show that this is, in fact, such an onerous time burden that it should usually be ignored, not on others, who must prove an absence (the lack of situations where it would be onerous.)Everyone preaching about what DMs should do almost never look at the in-game time. And when it is pointed out, they either hand-wave it by saying, it doesn't take long, or they insist on these non-realistic time perimeters, such as, "Our group's 8th level combat only takes seven minutes." Yet, when asked to show proof of any of this, they never do. They actually, never can.
Because I really don't think it's that onerous. More importantly, I think this is something that deserves a significant time investment anyway! This is the exact work that fosters player investment. Showing the player that it is worth their time to invest. Rewarding genuine player enthusiasm, perhaps the single most precious commodity a GM can get.
Further, as noted above, there are real dangers with using the kinds of short-cut tools that let you skip this sort of thing. Illusionism is a risk. I assert it is an unnecessary one; not only that, but that in general, not using these risky tools actually leads to more and better gaming, without being meaningfully more difficult to do. Some of it involves pre-game prep (e.g., preparing possible diegetic intrusions, a la "the god of goblins could intervene to save the goblin necromancer"), some of it involves developing your improvisational skills, and some of it involves being willing to confidently declare something now and work out what it actually is later. All of which are good, useful things to do regardless of your playstyle preferences.