THIS HAND OF MINE IS BURNING RED! FUCK YEAH!
Busou Renkin isn't much for the yelling, but it's there, and fighting does consist of "I'M LOUDER SO I'M STRONGER!"
Historys Strongest Disciple Kenichi. Again, not so massive on the shouting, but much fighting.
I think shouting as a form of combat died out in the 80s a bit.