I think good points were made on both sides here. On one hand, Ninja Gaiden wouldn't have near the legacy it does if the game had an easy mode. On the other hand, accessibility modes (sometimes an easy mode like Funky in Tropical Freeze or one-button mode in Super Smash Bros) can allow for a wider audience to engage. It's not an issue that some people can't play some games but it would be an issue if easy mode were mandatory. Taken to extremes, I would prefer all video games were too hard for me rather than video game companies be forced to include easy modes.
In many games, it doesn't hurt my enjoyment to have an easy mode and it allows other people to enjoy them, but in some it can take away from people's enjoyment. It's a personal problem to be sure, but that doesn't make it any less of an issue if many people have the same negative experience. Back in the day, when I was knee-high to a grasshopper, I ruined several games for myself by learning cheat codes. Risk is removed from Age of Empires II if I can just drop a Furious Monkey Boy or a Gatling Cobra into the battlefield on a whim. I have no incentive to beat a really tough level of The World is not Enough if I can just look up the code to skip to the next level. And then why not just skip to the end to fight the final boss?
I'm old enough to have cultivated a little self-control now and having the option to switch to easy mode just to kill that one deathclaw doesn't ruin the game for me (because I know that if I do, I'll use it on the yao guai and then the raider and then just to travel from place to place to make it quicker and then before long, I've taken the fun out of the game) but it does damage the experience for some people. The fact that somebody isn't self-controlled doesn't mean you shouldn't make games with easy mode and the fact that somebody only has one thumb doesn't mean you shouldn't make Dark Souls.