I really dislike the classic Monk fantasy (like Diablo or other unarmed fighter examples), but I love being a Pandaren Monk. Not necessarily because of the kung fu aspect, but because I really identify with the personality. The soft-spoken, unseeming Pandaren drinking his tea who suddenly appears behind you thwacking you across the head with a stick to teach you a lesson.
The 'Join me for a drink, friend!' mentality instead of the 'Life is Pain' DK approach.
I think it fits into the world just fine, but WoW certainly does cater it's theme a lot more towards a more militaristic or magical side. I actually started WoD as a Paladin because I just didn't connect with my Monk being this military leader in a spiky horde base (after a couple of weeks I went back, but didn't make me feel too much more at home).
But when it comes down to it, I just love it. Aside from having a great order hall and campaign (especially if you're Pandaren), I do feel like this wandering hero.
I must say that I did feel like Pandaren, and Monks, were being woefully unrepresented. We didn't even feature at all at the Broken Shore. The interesting thing I've felt though is that I've gone from wondering who's in charge to realising... I'm the Pandaren in charge. I do feel like the Monk leader now. I'm the one representing at Alliance meetings, I'm the ambassador, I'm leading the last remnants of a shattered order.
Thematically, I think non-Pandaren Monks might feel underlooked and dominated by this heavy alignment with the Pandaren. But as a Pandaren Monk, I feel like I've got a lot to fight for. A land, a home, a people to fight for. The Pandaren order campaign didn't focus on gathering great cosmic power, leading an army or an epic fight over the fate of gods and kingdoms - we were defending the innocent and rescuing our people who were taken.
Monks don't really fit too well into the military commander/warchief type role in my eyes. But leading an elite group of fighters like the Shado-Pan, infiltrating and disrupting enemy war camps, taking on dangerous missions, or just taking on the role of wanderer within the mystical broken isles? I think the class fantasy is being fleshed out a lot this expansion
Edit: That said, there are times where I get pissed that we have a pretty crap collection of leather transmogs available to us, and I do sometimes crave playing a class where I can just have badass armour and a kickass sword. No chi bollocks, just stabbydeath and heroic posing. But then I have a cup of tea and it's k.