Well, hard pass from me, then. Multiplayer modes I can understand. Aside from Nintendo, very few companies support local offline MP. But there's no reason why a single-player mode needs to require an internet connection to function
If your internet goes out, or the game's servers go down, or PSN goes down, you won't be able to play. It also means the game itself is essentially guaranteed to stop working one day regardless of the physical condition of the game & system. Once Sony pulls the plug on it, that's it. And since it's a racing game using licensed cars, that means it could last only a few years, seeing as GT6 only lasted for four years before reaching "end of service" (MS also pulls the plug on the online parts of Forza games after a few years, and stops selling them digitally).