I think what people should look at when it comes to challenge is what it is like to run a Dungeons and Dragons game. If you want your players to have fun, you need to encourage them to play smart, but at the same time you don't want them to die. It's no fun to take five steps and then die in the first encounter. You want there to be rising action. The first room has three or four guards in it capable of taking up 1/4 of the health and resources of the players if they run and gun, but if they instead explore and see that they can climb the rafters above and drop the chandelier on the guards, they can get by without a scratch. This will pay off when they have to fight the Minotaur capable of taking up 3/4 of their helath and resources, who is going to be next to impossible if they run and gun, and yet enough of a challenge even if they're at 100%.
Now, video games have checkpoints, and it is a good thing. Because I might go through running and gunning a room the first time, then die at the Minotaur, but when I start in front of the guard's room again I see I have more options open. Thus I learn that, later in the game, I should look for alternative routes.
I like the games best when I can get by with the skin of my teeth. The Halo, Gears of War and Call of Duty method of health and regeneration works pretty well for this, as it allows you to try, try again.
Some games, though, really do need to work on this. Devil May Cry 4's Human mode is a joke, but since I was new to the series it was necessary in order for me to complete the next difficulty mode. As I learn better ways to play, I find myself barely making it through some encounters, and it turns me into a better player.
Also, let's compare Mega Man 1 to Mega Man X. Mega Man 1 requires you to memorize each stage if you want to beat it, because otherwise it is impossible. Mega Man X doesn't, yet it still presents a challenge. Guess which game I love to pop in and kill an afternoon with even to this day?
While some games are too easy, I think people just need to suck it up and enjoy the challenge that's there. We're not all masochists, and even if checkpoints and recovering health make a game "easier" (let's see how many tries it takes for you to defeat General Raam on Insane), I get a game I can fully experience and extra immersion, too.