Two cricket teams are having to decide who fields first. Here's one way: the home side captain decides.
Here's another way: a coin is tossed, and the winner of the toss decides whether that team fields first or bats first.
The second is the way it's actually done. I don't think any cricket players or cricket fans would think that changing to the first way would not make a difference.
		
		
	 
That's such a bad comparison I don't even know where to begin pointing out what's wrong with it.
	
	
		
		
			A GM deciding that an action fails automatically is preventing the player from changing the fiction in a way that the player cares about (given s/he declared the action for his/her PC).
		
		
	 
The dice deciding an action fails does the same thing.
	
	
		
		
			A GM declining to "say 'yes'" to a declared action and therefore funnelling it into the action resolution mechanics is allowing the dice to determine whether the fiction changes as the player wants it to, or whether it changes in some other way more adverse to the PC.
The first looks like a unilateral decision about the fiction.
		
		
	 
It is a unilateral decision.  But having a unilateral decision maker about the fiction doesn't necessitate player agency is taken away.  As 
@prabe has been saying when this is done incorrectly then a lack of agency can certainly occur but it's by no means a required feature of such a system.
	
	
		
		
			The second looks like the playing of a game in which the participants are able, via the mechanical frameworks, to change the fiction in various ways.
		
		
	 
Just to be clear, "DM Decides" is a mechanical framework.  In such a game the mechanism for resolving actions is the DM.
	
	
		
		
			The idea that they are not different in respect of the capacity of various participants to influence the fiction is simply not credible.
		
		
	 
When your premises are faulty you end up at incorrect conclusions.
	
	
		
		
			Another way to come at the same point: if the GM gets to decide everything, player input is mere suggestion. It's like a monarch and his/her courtiers and advisors.
		
		
	 
The players have a distinguished role of being able to control their characters actions.  What your character "attempts to do" is part of the shared fiction. For that reason I don't agree that players are simply making suggestions in that style of game.  More importantly though, the GM isn't so much a monarch as he is an elected president with certain duties and obligations.  Those duties include determining success or failure when possible and setting a DC when there's too much uncertainty.  But  he is obligated to do so in a way that makes sense given the genre, other fictional constraints and anything else pertinent to the situation.
	
	
		
		
			In a structure of "say 'yes' or roll the dice" either the players get their way or the issue is rolled for. Rolling (or lottery, or other randomisation) as an unbiased decision procedure, which distributes the possibility of winning the issue over multiple participants and hence respects the agency of all of them, has a long history. Applied repeatedly - as happens in RPGIng - it is a way of integrating various participants' contributions into the unfolding shared project.
		
		
	 
And it's easy to see where bad faith play using that methodology can also destroy the agency of the other players and DM in that kind of game.  Necessitating a roll with a chance of success for all actions, even those for ruling the world / mass mind control / etc, all tends to destroy agency just as quickly as a bad DM intent on forcing the characters to do something.
	
	
		
		
			But this isn't even true. For instance, in Burning Wheel my character might be unconscious, and hence not in any literal sense taking actions, but I might be able to make a Circles check to see if an acquaintance, having heard of my plight, comes to rescue me.
		
		
	 
The issue is one of taking my term at literal face value instead of what I've pretty clearly been stating it means.  Character Agency = Agency of the Character = Agency over the character = Agency over the characters actions.  You seem to be confusing that with Agency over the fiction concerning the character.
	
	
		
		
			The focus on the character is just a distracting way of trying to approach the actual question, which is can the player meaningfully affect and change the shared fiction?
		
		
	 
IMO in terms of comparing and contrasting RPG's it's more meaningful than that.