They seemed to be trying for that with Season 2. There were a bunch of subplots all over the place, what with Saiou making Asuka and Manjoume his bitches, Ryo turning into Hell Kaiser, etc. etc. But they give all of the subplots besides Hell Kaiser so damn little time, it meant almost nothing.
Season 2 probably would've worked out better if they'd introduced the tournament earlier, had it be a bigger plot point, and left Judai out for more of it than they did.