If you are tanking then you are pretty much a designated leader. Say what you will, that's what it usually comes down to. If you have no desire to lead a dungeon run or take charge of a group, play a DPS.

Controlling the fight is the tanks job. And if interrupting is an extremely important part of the fight, then since you are the most important role in a fight (in your own selfish words, since you can obviously kill everything just being a tank and don't need a team) you should get the most important responsibility of interrupting.