Something I've considered since I made my post is that it may have been for a certain effect?
Just a theory but it could be that when the player first goes from 200%-80% health to 79%-60%, showing the first pain state without the nosebleed and then the normal status with it, it might have been made to look like a "slow bleed" from the nose during that state switch. That might be an interesting effect to add a touch more realism I suppose, however this of course is a problem with consistency as the player is still likely to get hurt or fire continuously while in 79%-60% health and the nosebleed will keep flickering in and out during that health state.
So perhaps it may have been done for an interesting, if subtle, effect here, but yeah, IMHO I still think it'd be a fair trade-off whatever the case, and having the nosebleed be there continually would both look better and be more in line with the mechanics of the rest of the face graphics.