The reboot definitely needs to focus on these aspects: performance, tone, customization and replayability.
I would gladly take 60 fps over 4K resolution. Saints Row 2 was horribly optimized on PC, they cannot repeat that with this reboot. Graphics do not mean sacrificing depth and attention to detail.
I want it to be comic booky/cartoony as fuck like the original. I like my gangs to be super color coded and drive specific types of cars. And I want there to be theming.
That's one of the worst things about newer GTA's. It lost all that charm by making everything grounded. All of the fucking gangs just blend together.
The appeal of the original Saints Row was its comical portrayal of gangsta urban conflict. It knew when to take itself seriously without downplaying fun. Its characters sold on its multi-layered story for city prominence.
Its intro setpiece says it all. GTA: San Andreas is to Menace II Society as Saints Row is to Don't Be a Menace to South Central. Its humor and gameplay was its charm.
Customization is Saints Row's bread and butter. Attire, cars, protagonist, weapons, all yours to do what you see fit. I have no doubt this reboot will spare no expense in that category.
For replayability, it should look at Saints Row 1 and 2 for that inspiration. FUZZ, Mayhem, Insurance Fraud, Septic Tank, strongholds. But don't lock progression behind activities. And no puzzles like that bullshit in Saints Row IV. PvP multiplayer would help wonders too, but it would need accurate, fair controls for it to be balanced.
All of that would make Saints Row satisfy that GTA itch AND put Saints Row back on the map as a contender.