I think it's the harshness that intrigues a lot of people who play Nuzlockes. Just the fact, that you could end up losing one of your favorite party members to some stupid luck is what makes it rewarding for them to continue playing that way. The drama that a loss causes makes their Pokemon more valuable and makes beating the game mor rewarding. For me it's just a cheap trick to hack difficulty into the games, though.
I've actually spend a good amount of time reserching the Pokemon games in terms of design. Knowing how they expect you to play the game, allows you to adjust things a little bit better. I suppose competitive play also helps, since that one is all about strategizing, coming up with a plan that allows you to beat your opponents team without having the options of items and higher levels. Basically, if you find a way to look at the games from a different angle, you get a lot more options. Like, if you're underleveled, you can make use of X items, which is something nobody makes use of, simply because they don't need to. On the other hand, X items are still one time use items, so you need to be careful with using them, especially when you're short on money.