Honestly, the base concept of this post is kind of a catch-22. Yeah, you can read your skills and such, you really should be familiar with what they do and all but there really is only so much you can learn outside of end-game content about how to play your job. For the most part, specifically in reference to your main complaint here, you're running mainly 4-man content in which case you will never get to experience 2 of the same tank or healer class together in the same content.
Yes, there's Bismark and Ravana that are 8-mans, and we have Void Ark now, but none of that content is really to the level where it's going to force the kind of 'perfect coordinated play' that is required in the hard end game content. Even Alex NM isn't going to really force you into positions of playing your role to its utmost. I agree, you should have an understanding of how your job works before taking it to that level, but there's no real good way to learn how to play a role in a specific composition for end game.... unless you go and play in that composition in end game.
Also, since you say that you hate getting 'paired up' with another class means you're doing DF stuff... which, first off, is DF so you shouldn't be surprised that you run into some bad players... but also the real end game content where you reeeaaally need to know your job is only available for pre-made groups at the moment.