It’s still unclear if/when they are going to fix battle shout threat. It did a lot more threat in vanilla. They claimed they were going to fix it when they nerfed demo shout threat, which was bugged to give a multiplier based on the number of mobs affected, but from what I’ve heard from some warriors, demo shout seems to be nerfed but battle shout didn’t seem to be fixed yet.
It has only been mentioned in the bug report forum here: Demoralizing shout is bugged and it is why we have this AoE meta - #64 by Aggrend-1483
so it’s not clear if all hotfixes involving these abilities are live or not yet, but they claim that they want the abilities to work just as they did in 1.12. Once that happens, you then would actually generate a lot of threat with battle shout. To the point that if you’re hitting enough targets with battle shout, every mob that has you on their threat table would essentially be hit with more threat than if you had sundered them, but it happens to every single one in one cast. It will be less threat than the bugged (and I think now fixed but I don’t have a warrior myself to test it on) demo shout if it hit enough targets, but still better AoE threat than anything else you have.
I don’t believe it’s working/fixed yet though.