Making tanks easier to play isn't going to incentivize people to play them. Tank mains typically enjoy tanking, and play these jobs almost unconditionally during their highs and lows. The instant queues are usually viewed as a nice bonus rather than the reason they play the role. Trust me, if the near-instant queues are not enough to get players such as yourself to give a go at tanking, rewards and nerfing gameplay isn't going to do it either.

I believe getting more players to play tank is by making the jobs themselves interesting and fun to play. The aesthetics to DRK alone is a big reason why it still has so many players leveling it and using it in endgame despite the uphill road it has had all of 4.0. PLD mains stuck with it despite their gripes in 3.0, and though I don't play PLD I hear the job is pretty damn good now. Very fun and feels like a PLD. These are just examples off the top of my head.

If you absolutely don't want to use a tank or healer to progress the MSQ, then your next best bet is a buddy who will tank for you or simply just wait things out like all the other DPS players.

Oh, and the average wait timer doesn't mean a whole lot. There have been many times I have seen the timer go well beyond the average time, and I have also the queue pop in far less time than the average when it is high.