The one genre I see as being stand alone/separate, is also the one with the most potential to outsell the main GT franchise.
GTSR or GTW: Gran Turismo Street Racing or Gran Turismo World.
An open world street racing game with multiple varying locals from city, highway, coast, mountain side, forest, valley ways, mega bridges, tunnels, and off - roading. All with varying levels of optional traffic, and courses with obstacles, divided lanes, and alternate routes.
With GT's physics and your typical "The racing depicted in this game is illegal and dangerous... Drive safe and keep it on the track" warning found in all street racing games. Drag, Drift, Touge, Kaido, Gymkhana, instant challenges, highway battles, point to point, rally cross, and some tracks with cross sections and jumps would all need to be included.
This game would label GT7, GT8, GT9, etc obsolete, null, and void for many a GT fan and would likely stand in direct competition with the GT series itself.
Sounds like a next-gen 'Tokyo Xtreme Racer' to me! Also, found and liked your thread.