It's an airline policy that the FAA has approved, so it carries the same weight as an FAA rule. All the FAA cares about is that the airline has policies that ensure that all carryon items are stowed properly for takeoff and landing. If US wanted to allow female passengers above some age to also carry a purse on board, the FAA would approve it. Why would the FAA approve it when there often not enough room for the current 2 items given the higher passenger loads today? Because US has a policy that carryon items that can't be stowed in the cabin get gate/valet checked. So the FAA requirement is met.

Jim