I think that the reason why people who are newer to FFXIV find WAR's lifesteal to be bizarrely out of place is because lifesteal is fundamentally a magical effect where you steal someone's life essence, and is typically darkness-elemental aspected along the lines of Drain/Osmose even within this franchise. The DnD Berserker concept, as an example of what gets done traditionally, is more focused around damage resistance and stat bonuses while Berserk. You might see Warrior types having a high rate of regeneration or damage resistance by just being physically tough, or using a battle cry to rouse allies, but you typically wouldn't see them vampirically draining their foes or magically weaving raidwide bubble shields out of thin air in any game other than this one.

And the only reason why WAR was grandfathered into vampiric attacks was because ARR may very well have been this game's last expansion, and so PLD and WAR's initial designs were never set up in anticipation for future tank additions. It took a tremendous amount of complaints from the playerbase for the dev team to prune WAR back such that other tanks could actually have some sort of an identity.

In short, it's just the legacy of a historical bad design decision that this game has never been able to fully erase.