Yes, it's been my experience that DMs who have not run 5e or who run 5e like other games ask for ability checks without the player describing what he or she wants to do. That is not how things are prescribed in D&D 5e. You don't get to ask for a check until I've described what I want to do, exactly as your "fundamental decision loop of an RPG" suggests above.
So we agree on what the fundamental decision loop of a traditional RPG is. Good. I want to make it very clear as to what my thinking is grounded in.
If I have had a player tell me I "don't get to ask for a check", that would be the only player whom in 30+ years of gaming I would tell to just pack up and go home now. I'm sorry, but your understanding of rules and processes of play is a little bit weird.
It's a wonder why you would violate the very loop you laid out there so succinctly, unless the game allowed for it.
I've read a lot of rules, and it's a very rare game which understands its own processes of play so well that it formalizes them to any degree. It's very typical for even highly detailed RPGs to have unspoken assumptions about the processes of play, or to give the participants in the RPG rules but no clear guidelines about how the rules are intended to be applied. That's one of the reasons you can see very varied games taking place with both tables believing (with some justification) that they are strictly adhering to the rules.
So for example, as far as I can recall, 3e doesn't actually specify how skill checks are to be made at all. It gives situations in which a skill check might apply, but we could write essays on the different ways different tables could apply the 'Search' skill check or the 'Diplomacy' skill check and what processes of play that they use that govern what happens before a skill check is made, or particularly what process of play a player must follow before they are allowed to make a search check to resolve some proposition.
All that aside, a skill check is a mechanic used to resolve uncertainty. That much I agree with. But there is no promise that such a mechanic has to be linked to an action, much less an intentional and declared action. Plenty of skill checks in every single system I can think of are not linked to any sort of action, but are in fact passive. I am not familiar with 5e, but I would be very surprised if 5e lacked passive fortune tests and lacked reactive fortune tests. I mean, you still make saving throws when targeted by a fireball in 5e right? You don't have to take an action to be targeted by a fireball.
Even a passive check follows some statement by the player about an ongoing task his or her character is performing, such as Keeping Watch while exploring the dungeon or dark forest which allows the character a chance to avoid traps (if in the appropriate rank of the marching order) or not be surprised. If they do anything else, then they have no chance and passive Perception does not apply.
Wait, what? So by that standard, it is not possible to have a check that doesn't result from a "declared action". The process resolution loop I just described is in fact a loop. That means every action is an ongoing action that follows from some prior proposition. In every case I cited of either passive or reactive tests, some prior action proceeded it and was ongoing. So if we can force a dice check on a player on the basis not of his immediate proposition but on the basis of some declared ongoing action, then your whole stand on principle makes no sense because there is no concrete principle to actually defend. Going back to my examples:
"Six limbed statue isn't merely a weird statue, but a statue of a particular agricultural deity the cult of which you are acquainted with.": This presumably follows as a result of some ongoing action to enter the area where the six limbed statue resides. Further, it's important to note that I'm not in any fashion asking for a knowledge (religion) check in an effort to deprive the player of agency. On the contrary, I'm trying to ensure that the player has the most agency available possible, by not making them pixel hunt for the right skill to ask for in order to know something that the player's character might already know. Ensuring that the player is making an informed decision is the opposite of depriving the player of agency. I'm not running some sort of Kraag Wurld.
"That tiled floor isn't just decorative, but is disguising a series of pressure plates." Again, follows from some "ongoing" decision to enter the room with the tiled floor. And again, I'm not trying to deprive the player of agency by making known to him things that his player should know. Obviously, if the player decided his character was going to put on a blindfold before going into the room, I wouldn't force him to see the tiles, but it would be wholly dysfunctional and passive aggressive GMing to deny the player passive perception abilities unless the player called them out as being in use.
"You here the sound of rushing water coming from the right passageway."
"There is a spider hiding in against the darkened ceiling of the room."
"The pipe tobacco he is smoking is an expensive brand imported from Multania, the same country the assassins two scenes ago hailed from."
Again, none of those things specify an action that the player is taking. They are simply unobvious information that a character might overlook, but which perceptive and knowledgeable character might not. And in all cases they follow after some "ongoing" proposition, because after the initial scene every check follows on an ongoing proposition. You never exit the loop.
Further, far from asking the players to make one of those passive checks, my usual process of play (and this might really blow your mind) is to
secretly make those checks on behalf of the player without telling them what I rolled for or what the result is. That's right, I don't bother to even ask the player whether they want to receive information from a passive skill! I don't always follow that process of play, because sometimes all that dice rolling in secret behind the screen isn't worth the effort, in particular if there is a very high probability more than one player will succeed, but that is my preferred process of play.
Incidentally, this is what I mean about processes of play not be hard specified by the rules. You won't find a lot of rule sets that require or don't require a passive skill check to be made in secret by the GM. Most of the time, a rules set will leave it up to the table to establish the actual process of play.
But even if I am incorrect on that point, many DMs still call for checks before the player declares an action. And since an ability check is a mechanic used to resolve uncertainty as to the outcome of an action, the DM is effectively declaring an action for the player. Which is what I object to.
Yes, I know what you object to. But I object to the claim that every fortune check imposes an action on the player and that every resistance test or passive skill check has to be first permitted by the player.
That's, not to put too fine of a point on it, nonsense. I'd slap you with the label "problem player" and be done with you if you showed up with the attitude that you as a player had some sort of veto power over when the dice were rolled. I've had some players that were a handful to GM, but none ever so bad as that.
Now, if you are really serious about this stand on principal and if you can find a GM that is willing to operate under those constraints, then great. But from this perspective your requirements not only seem impossibly high and self-contradictory, but utterly unreasonable.
Bottom line for me, based on my understanding of How to Play D&D 5e: Don't ask me for a check until I've declared an action, please.
I'm not even sure I understand what that means. I get all the words but I don't get how you actually play an RPG that way. Surely there is some test to resist things in 5e D&D that doesn't involve a declared action by the PC? Are saving throws forfeited unless the player first explains what he does to earn the saving throw? I can imagine that as a process of play, but I doubt there are very many tables that utilize it.
I wrote an essay on 'How to Railroad' once that I consider pretty good and even somewhat influential (in that it influenced the thinking of a lot more prominent writers than me), but at no point did I list 'asking for a check' as a technique for railroading. (
http://www.enworld.org/forum/showthread.php?298368-Techniques-for-Railroading). Feel free to try to explain how it is, because I'm not seeing it, or very many players that would actually tolerate it in practice. "I'm sorry. You didn't correctly explain what you were doing to ready yourself for this surprise attack. No dexterity save for you."
My position on that is the DM decides if and when the dice get used anyway. So if you don't want to stake a particular outcome, then just don't do that. But once the DM has decided we're rolling dice, they should fall where they may.
It's not as straight forward as that. Fudging can include all sorts of things, like for example deciding that those reinforcements that were supposed to arrive on round 4 won't arrive afterall, or deciding that that 110 h.p. monster actually probably still makes a good fight with just 90 h.p., or deciding that, yeah, now would be a good time for the monster to fail a saving throw or do half as much damage on an attack. I'm not saying I do that all the time, but occasionally bad design on my part meets bad luck on the parties part, and it's best for the game if I maintain the illusion of drama but fudge the fictional positioning behind the scenes. Also, can't the players decide to roll dice as a matter of course? I mean, at some point the players are going to understand the rules and the processes of play at the table, and they won't really need prompting for what dice to throw in response to some proposition that they are making. I'm not "allowing" the player to roll for initiative, for example.