It can be done but the current match finding system have to be tweaked with filters just to get it going and new items have to be added with skill tweaks just to balance it. In my design I separated PvP in two parts; brawl mode and PvP mode arenas, as in plural.
Brawl doesn’t require any conditions and consist of only one area. The treachery is it flattens out your paragon levels automatically and everybonus that comes from it. Nullifying all plvl won’t make Brawl mode any balanced (there are broken builds still), but at least it would be possible for low level pre-70 characters (preferably 52-60 or lower and banning one out of five skillrune types) to have fun with it without minding plvls.
PvP arenas are a bit of complicated and I call for plvl and highest solo GR clear while looking for a rival to determine the standard damage mitigation that applies to ranged and melee type players. With some thresholds, standard damage mitigation can be scaled up higher as plvl and solo grift clear of challengers grow with narrower brackets. As a competitive approach, PvP mode offer different arenas to be unlocked through achievements or achievement points and even allow player to tweak rulesets about; health globe spawn delays, refill conditions for pylon/shrine spawns, trap hazard triggers and so on.
As for regulating crowd control and health regeneration, you can introduce a small structure just like shrines or pylons in the arena, called wards. These structures can detect ultimate transform abilities (WotB, Vengeance, Archon, Champion of Akarat, Epiphany) that give you CC immunity and drain your health directly along the duration if you stand near their range and it damage you further depending on your depleted primary resource.
As match goes on, wards can gain more range and push their influence to cover most of the arena until they get somewhat reset by pedestals scattered around the map just like environmental hazards or refilling shrines. There are passive abilities and invulnerability frames to withstand ongoing control impairment chains and they’ll do just fine as long as wards are up and active.
Besides a filter for solo GR clear and plvl to determine damage mitigation game should support this motion by introducing crafted PvP gear that only activates their powers in the PvP arena mode. Said items can offer more damage against humans/elites while also having less damage taken from qualities to them. Such traits can be added to the less used skillrunes for instance.
Going further, you can create PvP based shields that ignore and nullify critical hits (hint: monsters can not score critical hits and thorns never crit) on block and other pieces that make nephalem glory last longer/refresh cheat death, gain cooldown reduction as health goes lower or grant absorb equal to a small percentage of thorns output. Things never can be balanced but can be made interesting.
As for rewards there can be bets for your duel winning streaks one on one with random casual matchmaking. What can you bet? I don’t know. What can you risk?
Such bets ofcourse will be disabled when doing a match between friends or invites. So there’s no possibility of abusing the system for bots feeding their multibox user mats, items or gold. Something so simple at the surface, not complicated at beneath either. Only if you read and think twice.
tl;dr: there’s a possibility but it won’t be a healthy approach to keep the old systems for the “old times’ sake”. They need tweaks to lessen impact of the power gap between player bases.