Is this really not obvious?
Fraud prevention. Paper certs without a picture are ripe for fraud as they are a magnitude easier to forge.
Just this week US CBP intercepted a shipment of fake vaccine cards.
Requiring two pieces of ID to be checked by a person who was hired for a service job adds friction, delay, error, inattention, disinterest, perfunctory review, etc.
Most folks making the review (restaurants, cinema, etc.) will prefer not to be the heavy and will prefer to get onto their primary business function.