I don't know if your registration is like ours, but here it's not a good idea to keep your registration in your vehicle for another reason.
When you sell your vehicle, typically you fill out the information on the back of the registration form and sign it, and the person who bought it takes it into the registry to register it in their name.
Here's the thing. They make you sign it nowadays when you're at the registry renewing. This means the thief has your car, and your registration with your signature on it. All they have to do is fill out the back and claim that you sold it to them and they're on the way to the registry to register it. Now it's your word against theirs.