I tend to go for the easy difficulties and play normal if I'm very experienced with the series. I play games for fun, not so much challenges.
I wouldn't necessarily say the two are mutually exclusive.
Case and point, I tend to play on harder difficulties because it's fun. Generally, I enjoy Hard difficulty- that is, whatever's after the Normal or Medium Difficulty (or whatever stands as the equivalent). Only in games where it's fun, though, of course. Persona's a good example of a series where harder difficulty really just means more grinding, since the game isn't exactly designed around playing separate difficulties and, because of this, the fun that comes with a harder difficulty is completely diminished. Similarly, Legendary on Halo is a good example of the other side, where the difficulty focuses a lot more on achievement than gameplay and undermines some of why the game is fun on its Heroic and Normal Difficulties.
But in a game where the game scales well with the difficulty and will require differing play and tactics to succeed, sure, because that means that there was actually thought put into the difficulty and how it would affect the game. This isn't to say that games that just increase damage taken and decrease damage taken (and various other mechanic changes) are bad, but developers really have to consider how it affects the type of game they're making.
But for me, the challenge is often the fun. When I'm faced with a challenge, it gives me a goal- it's not simply an obstacle, it's a trial, something I have to work through. The victory is more satisfying because it feels like I've worked for it- but more, the journey was fun as well. It's why I had so much fun with my Permadeath run of Wind Waker; every battle felt dynamic and personal, and I was constantly thinking of new ways to work through the constant slew of problems being thrown my way. The Souls series is popular (and fun) for similar reasons.
And this isn't a statement that easier difficulties are the wrong way to go about playing a game- there's no wrong way to play a game and everyone enjoys games their own way, but I do want to stress that people who play hard or insane difficulties or restrict themselves in some way rarely do it for achievement alone. Oftentimes they do these things because they legitimately enjoy it. And you may not have been saying that they're mutually exclusive, either, however I felt this was an effective way to answer the thread and reply to any future "I play for fun" comments that imply such.