And despite that, we already have a single unified clock standard that we follow!

Being able to measure the drift at a specific point doesn't mean it's relevant to computers timestamping their calculations. If a computer is ten nanoseconds off, that's basically the same as it being one rack to the left, or having some slack in the cable. There's no real effect.

Just syncing your clock once a day is enough to let you completely ignore the effects of relativity.