Dragon kick is useful team damage mitigation in magic heavy fights but it isn't absolutely necessary, just a good bonus. The difference can be negated with a little more vit. Personally I think you should play with what you want to play and what makes you happy. The Brd/Drg synergy is definitely a bonus if you want to play a Drg but isn't a deal breaker if not. I think the give/take is about equal either way.

The other option could be to have your Pally go Drk and you would have the Int debuff from there while still maintaining the Drg/Brd synergy. That is of course if the tank is willing/interested in doing that. Again though it more of a bonus than a necessity.

Honestly I think one of the really good things about the way this game is designed is that if the people playing know their classes well enough the party raid composition is basically interchangeable to a large degree while still providing synergy between other class combinations.

TL;DR
Go with whatever you perform best with and enjoy playing. By your post it seems like you want a reason to go monk and honestly the only real reason you need is because you want to. The loss of Drg/Brd synergy isn't going to make or break your team. Just play what makes you happy.