|why would you need to carry copies in your car. |
You don't need to prove ownership, if your pulled over, they are going to run your plates (and possibly the VIN if something seems wrong) anyway and it will come back as to who the owner is.
You don't carry the original insurance certificate, you carry the part that says place this in your car as proof of insurace.
You need to carry the registration, the REAL registration, not a copy. If you show them a copy, they are going to think something is suspicious. A thief can't do anything with the registration anyway.