Selective Availability actually wasn’t encryption but clock dithering. Messing up the time reported by each satellite introduced an error into the receiver’s esitmates of signal travel times, which caused a time-varying error in estimated position.
Now that SA is off, the largest error source is ionospheric; modernized GPS that transmits civilian signals on more than just one frequency will allow user equipment to estimate ionospheric delays, leading to improved accuracy.
Also, the new civilian signals will provide approximately 10x accuracy over the current C/A code due to their higher chipping rates. When Galileo comes on board, it probably will have about the same accuracy as the modernized GPS, and the increased number of satellites will further improve accuracy for receivers that track both constellations.
My understanding is that there was clock dithering to reduce the accuracy. However there are a few GPS channels. The low accuracy channel and the high accuracy channel. You need both to determine a high accuracy location. Selective availability is the ability to encrypt the high accuracy channel.
Civilian receivers tracking the C/A code are not as accurate as military receivers tracking the C/A and P(Y) codes. The reason is that the chipping rate of the military codes is 10x that of the civilian code (estimation accuracy is tied to the chip length of the pseudorandom spreading code). Modernized civilian GPS (and Galileo) will have codes with higher chipping rates, so will be on par accuracy-wise with their military counterparts.
However, the point about Desert Storm is that a civilian receiver (which military personnel could get) is preferable to nothing, since military receivers were in short supply.