Most of the savages fights aren't designed well with WAR in mind. The main exception to this is E3S where WAR is the best tank to bring into it. I can't comment on E4S as I haven't gone in yet (just cleared 3 yesterday) but baised off the numbers WAR isn't perfered in there likely because of tank swapping.
Here is the thing, WAR is kinda designed to be the MT at all times. Yes, they can OT but their effectiveness is reduced when doing so.
Reasons:
1) Vengeance still has damage tied to it. It might not be much but with IR affecting it as well as in the long run if you use it cooldown unless you need it for TBs you should be using it. Getting about 6-7 vengeance off comes to around 1320 potency or more if you are using it on cooldown not counting DH/Crits. Of course this can only be used on physical attacks so Leviathan ignores this. The problem is every fight is designed around tank swapping and if the WAR isn't getting auto attacked, well vengeance damage is kinda dead.
2) Nascent flash is a better MT skill than an OT skill. The 50% reduction on your co-tank makes even setting up a beefy nascent flash heal not noticable to maybe heal a boss basic attack, its good for you, but if your the OT the heal probably doesn't affect you as you'll be at full HP (except again Leviathan where you both are getting auto'd so its always good to use it on cooldown there). With a weak heal you have to look at its mitigation which is the lowest of all tanks outside of naked PLD interventions, but PLD has the option of using a cooldown they don't need to buff it to the highest giving it flexibility.
3) Raw Intiution is the best MT skill identity cooldown in the game. Simple as that. 20% mitigation on a 25 second cooldown with no need to worry about job guage or resources? Yeah its the best for TBs making it easy for a WAR to surive a tank buster with a good chunk of HP when paried with another cooldown (if you even need to).
4) Holmgang is still a thing. However, the issue with this raiding tier is 3/4 of the fights tie a required tank swap debuff to the Tankbusters now. Leviathan is however a short debuff so holmgang lets the OT not worry about requiring to share Tankbusters (except 1). E2S doesn't have a debuff tied to it but both tanks will always get hit by the tankbuster so using an OT skill during that on your other tank isn't advised... except for PLD because intervention works well with those kinds of tankbusters mitigating the most damage by far of all the tanks.


WAR isn't designed well for this raid tier I would argue outside of Leviathan and even there one of its damaging skills is gimped because its all magical. Its a small problem but it adds up when its personal DPS isn't very good and personal mitigation doesn't matter too much when you are forced to tank swap anyways.