Ask HN: Why aren't more contact tracing apps using GPS instead of Bluetooth?

Many contact tracing apps are only trying to use Bluetooth to decide which devices you're near. Is that really a good approach? I don't think so. It doesn't really matter if you're physically near me, if I cough on something and an hour later you touch that, you're very likely to get infected. Shouldn't the apps trace a persons movement? Then once a case is encountered ping all the individuals who crossed paths? The persons movements wouldn't necessarily have to be sent to a central server, they could be stored locally. Are there other concerns or limitations that I'm missing?