Because bosses don't just stop damage after they use a big hit.
Let's take Mountain Buster for example. It does baseline (without any CD's) ~4400 damage. and it comes with an auto attack that does ~850 damage. That's a total of 5250 damage. Following Mountain Buster he will generally attack once (sometimes twice).
So if we get a Mountain Buster + AA, and then another AA that puts us at ~6000 damage takenin a 5 second window.
A paladin in shield oath ONLY and NO COOLDOWNS will take 4800 damage, mitigating 1200 damage, and requiring 4800 to get them to full.
A WAR, assuming they don't yet have Relic +1, will be healing for 1100-1300 non-crit. This leaves the WAR also requiring 4800 to get them to full health.
This leaves them on even footing. Both will take the same time to get back to full because both will need 4800 healing and WAR will not have any healing bonus likely until 5 seconds later. Even assuming the boss does no additional damage in these 5 seconds this is where the warrior begins to fall behind.
Now that the WAR is slowing building stacks back up (it takes at least 15 more seconds to get back to max). Over these 15 seconds a WAR will average ~9% bonus healing. During these 15 seconds the tank is going to be taking damage. While a PLD will be taking 20% reduced damage, and thus requiring 25% less heals. The WAR on the other hand is taking 100% of the damage, but only has a ~9% healing bonus averaged out. Over this time period, average out, the WAR is at a ~15% disadvantage in healing. Meaning it takes the healers 15% more healing to compensate for the damage.
This means (potentially) 2 things: More globals in order to get the WAR to full before the Mountain Buster, and more mp spent by the healers.
This is a rather "dry" analysis because it ignores 3 important things, Block, Crits, and Cooldowns. Still, looking at those doesn't really help the position of the WAR.
Actually, Hiir is right on this aspect. Berserk is a tanking cooldown because it increases our heal from Inner Beast. Infuriate is also a tanking cooldown. Foresight and Bloodbath are extremely underpowered, but Berserk and Infuriate shouldn't be ignored as tanking CD's.
You are so off on all of this man. You really don't have the end-game experience to have an accurate picture. 25% of all the damage you deal? Yes, Warriors deal decent damage as a tank, and worse our highest DPS rotation (incorporating Fracture) is lower threat, which can be an issue on hard fights. But just using myself as an example: As a WAR tank I do ~100 DPS (this is using Unchained and Berserk as DPS cooldowns, which shouldn't really be done in real combat). I would say my rotation is pretty good. Not perfect and my gear could improve, but 100 DPS is good for a tank. It's 2/3 of what a "good" dps does at my gear level, roughly.
So 100 DPS over 30 seconds = 3000 damage. 25% of 3000 damage is 750 health.
Bloodbath is a 750 health HoT over 30 seconds under ideal circumstances on a 90 second cooldown. That works out to roughly 25 health per second, obviously. If there is any way to characterize this, it definitely not "a lot." It's worth using every cooldown, obviously, but it is a minimally effective cooldown.
Also, Featherfoot is the second (maybe 3rd on some fights) most valuable off class skill we can get. Why you would not run it in favor of Vengeance (which is a class skill so why is this in competition?) is something that baffles me.