I couldn't care less about damage modelling, seriously.
Better weather implementation, especially snow and rain. Rain feels lacking in GT5, in both presentation and physics. Snow was fun, but still could've done better.
better track surface collisions, especially dirt and wet surfaces.
Wind/air resistance, especially with non-racing cars.
A much, much better A-spec. I realize that a career in racing isn't exactly as fun as any mission or goal-oriented video game, but let's be real here. Gran Turismo is still a video game, therefore a constant race-after-race in A-spec is sometimes no fun. The transition between Beginner to Expert should go above and beyond a simple car change, if PD desperately wants to mimic real life. It goes against A-spec sim, but since we aren't really getting Arcade/Sim separation in A-spec, at least have some bonus objective-based game modes like "Try to finish at EXACTLY 3rd place" or some oddball that could be considered "fun" in terms of it being a video game, i.e. "Can only use brakes 5x in race.", "Speed limit of 200km/h for all cars", "Only lowlights during night race", etc.
Remove NASCAR. Just, remove it. Some people find the fun in infinite left turn high-speed racing but I'd rather take dynamic circuits with elevation changes and whatnot.
Expand on F1, drifting, Rally.
Add bike racing. Motor bikes, Dirt bikes.
uneven wet surfaces. Some areas should be wetter than others, after a rain/drizzle.
optional ANNOUNCER voices during race, just as for any other sports video game out there.
Car creator, barring the nuances like aerodynamic design or whatnot. More about aesthetic than performance.
More intuitive UI. Less clunky and crowded. GT has always been about sophisticated, even concrete feel of the UI but sometimes people want to be funky or hippy or whatever fits their mood.
Live radio stations while driving (disguised using an internet stream like Shoutcast, since PS4 has another chip for Download/upload).
Better car sounds.
Trim the number of cars. Seriously, just trim 'em.
Smaller, tighter tracks for the slower cars.