Cyclist usually isn't lucid to give their account. So the cops interview the car driver. Guess whose at fault? I've had this happen to more than one friend, despite other witnesses. One currently fighting a $200k medical bill because insurance thinks the driver will cover it, drivers insurance pointing at the police report saying they aren't at fault, etc.
It might work out in the end, but its a lot of pain and uncertainty.
My understanding is that the initial police report can carry a lot of weight in these situations. The fact that you weren't lucid on the scene also suggests that you may not remember the event, whether that's true or not.