Few things:

1.) First off, you're in the right. Some tanks are bad and when those bad tanks get behind the wheel of WAR, they start cruising around like a taxi driver in New York. There's no fixing that level of bad (at least not within the time limit of the dungeon), so you're better off just leaving and re-queueing when you can. You can stick it through, but it's going to be a painful run.

2.) Deliverance is actually amazing for trash when used correctly. Ideally you start off in Defiance - this gives you a stronger Adlo/WhateverAstroDoes and/or a stronger Stoneskin. Initial enmity is very important as well, so you definitely want to gain that lead before switching stance. Usually what I'll do is use my 5 stacks from Infuriate on Unchained if it's available, pop my offensive buffs + Bloodbath and then switch to Deliverance. When I'm in Deliverance I'm 24/7 spamming OP, this makes my health bob up and down a bit but due to the low damage each mob does vs how much I'm healing for on each mob. I'm basically not even in need of any healing outside of a Regen or fairy heals, it's pretty ridiculous. On top of this, I've got CDs like Vengeance, Thrill + Conv, Foresight, and RI + Awareness to smooth damage out with when I'm not in my tank stance. However, sometimes certain CDs won't be up, and in those cases you need to stick to Defiance - it's a very delicate balance.

3.) Deliverance tanking being amazing doesn't mean it's always the best option for your group. If your healer tells you to turn on Defiance, turn on Defiance. There is absolutely no sense in being stubborn about that, you're in a party, you're part of a team, you want to work together and the best way to do that is to listen to your team members. Not everyone can pull off Deliverance tanking either, it takes understanding of your job and how all your skills function together in conjunction with your healer's spells.

I'd say you have an understandable worry when paired with a WAR that goes Deliverance. If I were in your shoes, I'd worry too. I suppose the best thing to do is just hope and pray you don't get a bad tank, unfortunately.