Yes, it is very important to hide your car ownership and car insurance paper somewhere safe in the car because it contains your house address and if your car is stolen, the thief wouldn't know your house location. But there is one disadvantage to hiding your ownership and car insurance paper, which is when the police stops you for any reason, they would ask you for the ownership and car insurance papers. At this time, you must left the police office know that you have hidden your papers at a specific location and then ask him for permission to reach for it. Do not move your hands without getting permission from the police officers. Any weird move could prompt the police officer to interpret your actions as aggressive and dangerous which will make the police draw gun on you. So always inform the police about the whereabouts of your ownership papers and car insurance papers.
It is a good idea to leave the car ownership papers inside your car somewhere safe so that if any one of your family members were driving your car and were stopped by the police, they can retrieve the car ownership papers. The ministry of transportation in your local area will only issue one piece of car ownership paper for you and the photocopy doesn't count, as once a friend of mine told me that a police officer mentioned that to him before. Whereas for your car insurance papers, the car insurance company usually sends you extra copies for you to keep. You can also keep photocopy of the car insurance paper without the need to keep the original. Sometimes you can phone your car insurance company and ask them for extra copies of the car insurance papers and they would be glad to mail them to you.