We'll ask ourselves: what is intuitive? Often for designers, it means "familiarity". That is, users are assumed to have experience somewhere else and if THIS looks like THAT, then users can start making assumptions about what things are, and can have expectations of what will happen when they do things. But what's closer to real intuition is, is it easy to learn? I think this can beat familiarity, and the original Google interface (from years back) did that. You could type something in. The search buttons were obvious (though the gambling button was confusing, but it was optional so nobody cared). And you can't really do it wrong. It's a patient interface, doesn't break the back button, users can try all sorts of things just to see what happens. Undoing (and re-doing) is as easy as doing.
We'll ask ourselves: what's simplicity? Often for designers, it means "clean" or "less clutter". This can be a good thing. If a page or a site or an application does one thing and does it well, it should focus on this one thing and people will usually know what it's for.
But hiding things in order to make things "cleaner" or "simpler" is something people do sometimes, in a way that prevents users from discovering useful functions, help, explanation or quicker ways of doing the things they're already doing. So long as this stuff is discoverable (yet still out of the way if it's not expected to be used a lot) it's generally okay.
I read recently of an example of a program which took many clicks or stages through a menu to turn on and off a feature. The builders assumed few people would use the feature, and if they did, they would want it on all the time: meaning, setup would be a one-time thing, so letting it sink deep into the interface was ok to them. Instead, the deep menu prevented people from using the feature, which actually had many more and wider application than the builders had assumed. People thought sometimes that the feature wasn't even available, and you can imagine people may have gone to the competition who had this feature a bit more prominent or easier to get to. Simplifying the interface by reducing available options per level wasn't the best way of designing that one there.
This stuff's hard, and interesting as heck!