They do (that's literally how GPS/GNSS works), but they drift, for various reasons. One of the parameters that GNSS networks broadcast is a clock correction (how far off each individual satellite's clock is, how fast it's changing, and how fast how fast it's changing is changing), and those parameters come from the ground stations.

It seems like a little drift shouldn't make that much difference, but keep in mind that the speed of light in a vacuum (or air) is about 1 foot per nanosecond, so for every nanosecond one of those clocks has drifted, that's a foot of positional accuracy you no longer have...