If you prefer to pay for someone's damages to their car after a car accident then there's nothing illegal about that.
You don't always need to report the car accident to the insurance company especially if the damages are not a lot and you can afford to pay the person out of pocket to repair there vehicle.
I've damaged someones front bumper and headlights when I accidentally backed into their vehicle and I just paid them directly out of pocket and we never alerted the car insurance company.
So if you want to pay out of pocket for your own car damages or someone else's and leave the car insurance company out of it then you can do so.
You just need to report the accident to police if the car accident happened on a road.