But if in any of these games the DM runs the game like it's some other game, it will annoy me enough that I will quit. Running D&D 4e or D&D 5e like previous editions, for example, is just not going to fly with me. These games have rules which demand different approaches and, though some DM approaches are universal, not all of them are. So if, for instance, the DM is calling for ability checks before I have declared an action like we're playing D&D 3e, I'm just not going to stick around. In D&D 5e, I get one role: Describe what I want to do. The DM doesn't get to take that from me, either directly by declaring actions for my character or indirectly by asking for ability checks when I have not described what I wanted to do.
Interesting. I haven't run 5e yet, but I have run earlier editions and other gaming systems, and I run them pretty much all the same. My theory of DMing goes something like this:
DM: Here is the setup.
PC: This is what I want to do.
DM: Pass this fortune check to succeed at your action.
PC: I do/don't.
DM: Here is the new setup.
That's what I consider the fundamental decision loop of an RPG. The player makes a proposition in response to the scene setting. The DM adjudicates that proposition. The player then proposes a new response to the altered fiction of the scene. I think from what you are saying, that this is what you want to happen.
As far as I'm concerned, that's a pretty darn universal approach to the game and while I can think of some exceptions, earlier editions of D&D
are definitely not exceptions to that setting->proposition->fortune->resolution cycle and I'm mystified as to why you think that they are. In no fashion do I understand how "declaring actions for my character" is the same as "asking for ability checks when you have not described what you want to do".
I never declare actions for a character barring unusual exceptions like failed insanity check, possession by a spirit, or magical compulsion, and even then I prefer to let the player play it out (with the understanding that a player will be mature about it and actually act according to the situation).
But I all the time call for ability checks with no feeling that I've violated that.
For example, passive awareness is not dictating an action to the player, but does involve asking for an ability check despite the player not describing what they want to do. I might ask for various intelligence, knowledge or perception checks to represent what a player might passively recognize based on simple observation. That is there are some checks that alter how I describe the setting. This 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. That tiled floor isn't just decorative, but is disguising a series of pressure plates. You hear the sound of rushing water coming from the right passageway. There is a spider hiding 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. All that requires checks of your ability without dictating what you did. Passive charisma works much the same way. Those elvish snipers normally shoot trespassers first and then ask questions, but they like your looks and a passive reaction check causes them to decide to hail you in elvish first before letting loose their missiles. In no way if I do any of that do I feel I've violated your agency as a player. Are you disagreeing?
Likewise, sometimes things happen to a player first. Sometimes the setting itself has agency that it acts on. Suddenly the floor begins tilting wildly, and you must make a dexterity check to keep your feet. You can respond to that scene and tell me what you want to do, but first because something is happening to you, your position in the fiction must be determined. Again, in no way do I feel I'm violating player agency in requesting those rolls, especially if I've written down something like, "If any player advances more than halfway into this room, it begins tipping rapidly to the north, and a test of balance is required if the player is to keep their feet and not start sliding to the north." Again, I don't feel I'm invalidating your choice if occasionally something happens to you that you didn't want to happen, provided that what happens is reasonable for the scenario. I suppose in the case of these tests, you could always object, "But I want to fall down and start sliding.", but in response to that I would simply say, "Well, you pretty much always have the option to deliberately fail a reflexes test if you don't wish to try to pass it. Just let me know if you want to fail."
Again, am I misunderstanding you?
Along those same lines, if the DM fudges or pulls punches when an outcome he or she doesn't want to happen is likely, I'm going to bail if I notice it.
I very rarely fudge or pull punches, and if I do its usually to avoid a TPK where I don't feel a TPK is good for the game. I would consider it a failure of my technique as a GM if a player ever knew when I'd pulled a punch. But I have a habit of very deliberately rolling in the middle of the table (rather than behind the screen as is my usual practice) when making a roll upon which the life of a PC or a major NPC depends, so its not like I'm definitely not a 'let the chips fall where they may' sort of GM. I just think there are times when the dice are dictating something no one is going to find fun or reasonable, and I feel empowered to ignore them some of the time.