It would be cool if there was “A race is about to start, would you like to join?” and when you click yes, all previous data is saved, and you start over (on the stats front) “Please make you way to the start line”.
You also get presented with a different HUD (like you do with workout mode) Race mode. From there you only see things like who the race leader is, who is in the race, time splits etc.
This would mean that everyone is on the same course but some are riding, some training, and some racing.
This would keep the community feel that may be lost if private races are developed.