Should one tank in tank stance?

[Seraphor]

I consider tank stances to be a tool. For all 3, they're useful when you're learning new content (or still gearing up) in order to provide you with some safety net, but once you've mastered the fight, you shouldn't really need beyond the initial enmity rotation. The only time this becomes a problem is on longer fights in PUG content where the DPS don't use their enmity dumps. Grit is also unique in that DRKs need it to use Blood Price, so it's essential to use on a packs. PLD and WARs don't have that restriction. With that in mind, tanks need to use their cool downs more. I've seen this as I level the healers. I've started telling tanks who are new they really should use Anticipation on cool down, as it will be available every other, if not every pack. I notice people tend to save the CDs for boss fights and tank busters, but there's more than enough tools to handle those in non savage content.

Unfortunately theres not much space on xhotbars for all of the roles skills, and most tanks I know, or at least DRKs, choose Awareness over Anticipation.
In real terms, in the perfect situation, they each translate into a ~4% mitigation.
However, Parry is only valid against physical attacks, and Crit is checked before Parry (if you receive a critical hit, it can't be parried) so there's no point in using both at once.

In addition, WAR require Awareness for Raw Intuition (probably why they save it) and I believe PLDs base parry rate is lower to account for shield blocks, so Anticipation isn't as effective for them. (probably why they don't use it)

If you're playing with keyboard and mouse then sure, it's free mitigation, when it works.