It seems reasonable that we could just eliminate having to carry around physical IDs altogether (at least as a requirement of the law) and have the police taking pictures and/or typing in a name to verify someone's identity.
Neat idea but it misses a lot of practical problems.
Many police cars are equipped with cameras that can read via OCR your license plate (called "Automated License Plate Recognition" or ALPR) and check against a database to see if your car has been reported stolen, is reported in an Amber Alert, etc.
However, the person driving the car is a totally different issue. Let's assume that there's no requirement that you have a personal driver's license.
The officer pulls you over for speeding and he/she says, "name please?" You say "Oliver Klozoff." Without that government-issued ID you can make up any darn name you want to. That officer has no way to get you to produce your real name, even if it is Osama bin Laden and you're driving around the country touring Whataburger locations. Oliver Klozoff isn't an owner of that car? Well, your friend lent it to you for the afternoon, what's wrong with that? So without the fact that driving without a physical license is a crime, the cop has no way to figure out if you are a wanted person or not. Not a great thing for catching wanted people (see Timothy McVeigh and his traffic stop arrest after the Oklahoma City bombing for example).
On the flip side of civil liberties - the officer pulls you over for speeding and he/she takes your picture and runs it against a visual database stored by the DMV. Unfortunately, because it's nighttime and lit only by the officer's flashlight, and you grew a beard since you had your driver's license photo taken and put on some weight, you are no longer recognized as a valid driver in your state. Why not arrest you just to be sure?
You get the idea. Think of a driver's license like a form of two-factor authentication. It's not the physical card itself which is important so much as that it is a token which only you are supposed to have, which links you back to a known set of credentials at the state level which can be attached to a permission to drive, a known wants/warrants record, or so on and so forth. Just like how your physical passport isn't what is important when you enter the country - it's just a good way to get started when they scan it into a database where the real information is stored that can figure out who you are.