If GT were to have some kind of open world, what I think would be nice is a huge photomode map, or a homeworld.
When I mean by homeworld I mean having a actual garage you can drive in and out of and have locations around you like a perf shop, or a race center, or even a GT AUTO shop. Similar to the good old map on GT1 - GT4 that you could drive actually on. And for the people who don't have the time to drive across the city can just open a map and select what they want and teleport instead.
Similar to Test Drive: Eve of Destruction. It's homeworld is tiny, but it's a really nice feature.