The lore of madness fits right in with the invasion system, though it doesn't exactly convey it as well as it could if they had kept the "mad phantom" mechanics from DS3 in ER. I suspect they may have originally planned on it and then, for whatever reason, they decided to scale back the multiplayer stuff and make it as basic as it's ever been in the series.
The way the mechanics fit the lore better for the typical "bad red man" is the Volcano Manor faction. They literally introduce you to invasions through them (even tho they do also do the same with madness; the first time you might be invaded by an NPC phantom is in the madness village overlooking Morne Castle, and Edgar also invades you at the Warmaster's Shack after he goes crazy).
If they had purple phantoms in ER, I guarantee Edgar and a few other random invaders would have been purple instead of red.