If dungeon finder puts you in an unwanted dungeon, start specifying what you want to run. It's easy. You miss out on a couple of points for gear - so what?
I am not the most active of raiders/dungeon runners and I have zero problems with getting gear. I run instances/raids for the following reasons:
- I have not yet completed it as that role (eg I have not yet run many heroics, or my tank wont run it anymore, but my healer will)
- I have completed it, but want to practice a specific mechanic
- It is a training run for a healer or tank
- I am being sociable
However even on the very limited (in comparison to my peers) dungeon runs I have still managed to get a badge piece.
Easy fixed. If random dungeon finder doesn't give what you want, choose your dungeons.