That’s kinda sorta the point, though. If you fail to Hunt, the Monster gains on you - in the form of Stages, in the form of additional health and firepower (And size. For some reason.).
Armor is there as an equivalent to the hunters’ Strike system. If you chew trough the armor, you’re dealing permanent damage to the Monster, where Hunters have to die to go down, get a strike (Providing we’re not playing with Laz and his additional niche) and get up or outright die.
If you don’t deal significant damage to his health by S3, you’ve been outplayed. Simple as that gets.
And Wraith, due to its low health and armor, is the easiest monster to fight at Stage Three. Where Goliath, Kraken and Behemoth can just go nuts at you on S3, half health, armor or not, Wraith has to constantly rearmor, giving you a good chance to run down the timer, or get locked in a fight it may very well lose.