There are three classification levels in CA, depending on the conditions:
Requirement One (R1): Chains, traction devices or snow tires are required on the drive axle of all vehicles except four wheel/ all wheel drive vehicles.
Requirement Two (R2): Chains or traction devices are required on all vehicles except four wheel/ all wheel drive vehicles with snow-tread tires on all four wheels.
(NOTE: Four wheel/all wheel drive vehicles must carry traction devices in chain control areas.)
Requirement Three (R3): Chains or traction devices are required on all vehicles, no exceptions.
Caltrans Winter Driving Tips Chain Controls
I think the idea is that with heavy traffic flow, one car that gets stuck because it can't make it up a hill will cause massive traffic delays for everyone. It is geared at the lowest common denominator, meaning someone with bald tires from the coast who has never driven in the snow trying to drive in the mountains.