Why do you think potentially self-incriminating self-surveillance is "crazy" when you also think lying to the cops and other involved parties about what happened is bad? If you believe it's important to tell the truth in these situations, you should have no problem providing your own recordings of a collision, regardless of who is at fault.

Or is your point just about the cost of the dashcam being "crazy"? In that case, hypothetically, what if your insurance company cut you a check to buy a dashcam of your own choice and install it on your car?