Not all easy modes are created equal. If your game is , as the example in the article states- a cover based shooter and the easy mode removes the need to use cover then it's not the player who failed, it's the designer.
I feel like difficulty should be a more organic experience underneath the hood of a game. Give the player the option of adjustment after 3 failed attempts at any task like devil may cry had years ago. Do not penalize the gameplay scope just to make the game easier either, perhaps place a "trainer" behind the scenes that records how you play - how much damage is coming from certain enemies , how quickly you manage to do certain things, etc etc.
An example- let's say you're playing a game like gears of war and you get to a big open area with tons of cover , the game starts up an encounter for you. Now for a more experienced player- there's an obvious corpse holding a sniper rifle right near the start of this room and the enemies are coming from the other end with no easy path to you, in other words you are aware that grabbing that weapon will help you clear this room faster. For not so astute players, they might start just randomly going into cover options forgetting the gun. At this point the game would drop hints for the second player, maybe Dom starts shouting "sniping these guys would make this shit a shit load load easier man, shit" (gears of war dialog) and if the player starts moving and looking around and finds the weapon great!, should you keep getting shot for say another 30 seconds then perhaps Dom or Baird or whoever would run back to the location of the sniper rifle and shout "shit man, there's a sniper rifle and some ammo back here, come grab this shit" at which point the player would be alerted on their map as well. Moving on- the same player is now using cover and a sniper rifle to shoot guys across the map, but let's say they miss a dozen shots in a row, well at that point the difficulty monitor could step in , perhaps one of your team mates would say "shit man, just focus and pop those mofos", then when you'd open the scope the whole game would slow down and let you get a sure fire shot off, after killing a few dudes the game would speed up to normal again and a team mate would announce "got your head back in the game now ?".
This to me is the sort of scenario that works best for harder games, teach the player more skills rather then dumbing down the experience. Slow down the pace of the game temporarily to give the player a chance to keep up with the game.
This obviously wouldn't work with every single game out there but I feel is a better step in the right direction then simply having an "EASY" option where you get unlimited health or the enemies all die in 1 hit.
Just make sure that the player never has to re-do any segment of your game lasting more then 5 minutes at any point. If the player does fail (which will happen occasionally regardless) the harsh penalties present in 8 bit software only serve to frustrate in this day and age.
As far as only playing games for story... well It's not as though I dislike this option , I feel there is a small audience out there for it. I just don't "get" it, games are meant to be played and I kind of wonder why anyone would bother with the medium if they dislike the biggest portion of the experience but to each his own I guess.