The problem is that you'd still turn against Tyrant for the Incarnate system - that's the way it's been set up.
Praetoria was never planned, designed or set-up to be a new faction, or a 1-50 levelling experience - it has no special ATs, power set or zones, unlike blue and red side, and the storyline is written to strip away the lies of Tyrant, and get players out of his reach and into the normal game world by level 20.
If red side,. which is a genuine faction, with its own ATs, power sets and 1-50 levelling experience doesn't get its own Incarnate Trials, and has to tag along with the blue side, then the chances of the loyalists getting their own Incarnate Trials are close to zero.
The moment the Vanguard showed up, alogn with Arachnos and the Crusaders starting to high-five eachother, that was the end of any hope of a non co-op Incarnate Trials - by uniting the 2 player factions in the fight against Tyrant, the devs made it clear that Tyrant was supposed to be the enemy of everyone - kinda like we all fight the Rikti, no matter what alignment we have.
If Tyrant had made an alliance with Recluse - by planning to use him to open up a second front against Paragon City, and then destroy him later, while Recluse would be hoping to use Tyrant to defeat the Heroes of Paragon City, and then defeat the Praetorians himself - then that would be a big clue that the devs were intending to add some evil Incarnate Trials in the future.
And all the lore and other info we've gotten from I20 has just reinforced the idea that Tyrant is the bad guy that we all need to defeat to be able to face even greater threats in the future.
The devs have mentioned separate Incarnate atory arcs and missions as a potential alternative incarnate path - but those are still way more likely to be anti-Tyrant, because of the way the story has been set up. Incarnate story arcs and missions would certainly give an evil option for Incarnates, as they wouldn't need to be co-op - but the enemies would still very liekly be Tyrant and his loyalist thugs, because they're the major evil force we're all fighting against.
Resistance to Tyrant is the only option in GR, no matter what path you choose.