Guild Wars 2

I think the warrior is viewed more of an out going damage class so your trait feels more of a guardian trait

health/adrenaline and endurance all together is asking too much. if it were to be implemented I think they might make the numbers 10% of what you suggested

Probably a 45 seconds cool-down and a reverse skill of berserker stance
grants defense or heal and reduce outgoing damage for its duration.
something like protection, regeneration and weakness (only the damage not endurance penalty)

I have seen shout builds all over and thought why is everyone ignoring stances. Then I tried to make a stance build and found out why.

In their current forms stances are not viable. they last for a short time and have a long cool down so while a warrior might benefit from a stance will probably try to take advantage from other traits or skills before ending up having to use a stance

Should stances play a significant role in warriors like shouts do or they are just situational modifications to builds?

I think stances should be of equal power to shouts and play a bigger role like in GW1.

There are many ways to buff up the stances to make them more relevant:
More traits to buff the stance maybe reduce cool down by a percentage
Trait that gives another benefit to stances like shouts give adrenaline
Change the way stances work (weaker version) to be toggle type and one of them is active at a time like the elemental attainments

and I think traits that traits that use stances like last stand cool down should be reduced to match the skill itself