So Crota's presence prevented you from regenerating health…

I wonder what Oryx's presence would do? How wild would it be if your super, grenade, and melees didn't recharge at all? Can you imagine no supers, with the only way to get your grenade or melee was with gear that reduces your grenade / melee cooldown on certain actions? Suddenly army of one would be very desirable! You'd have to use something like bad juju to charge a super, then generate orbs for your team, which they could use to charge their supers and other cooldowns through perks.

Then again, it could be even crazier…

Could be interesting. In the same way that Crota's hard mode made those "regenerate health when you pick up an orb" armor pieces suddenly desirable, when previously that had been a perk no one cared about. Although currently, things like Bad Juju and Army of One aren't ignored to the same degree that perk was.