Generally, your declarations page isn't meant to be proof of insurance in such situations. It's advisable to always have your physical insurance card handy in your vehicle, or a digital version where allowed, to show to law enforcement during traffic stops.
For situations where the Department of Motor Vehicles or your lender requires proof of auto insurance, a certificate of insurance may be necessary. This document, while similar to a declarations page, excludes specific details not required by third parties, such as your auto insurance premium.