After a bit of digging, it seems that the downlink sensor feed (e.g. video) is the only part that is not encrypted (or at least it wasn't as of 2009 for first-gen military drones like the Predator, although at the time it sounded like they were looking into adding encryption for the downlink). The control uplink is encrypted.
"The command and control channel is, and always has been, encrypted -- because that's both more important and easier to manage." https://www.wired.com/2009/12/insurgents-intercepting-predator-video-no-problem/
"The theory is that we encrypt the uplinks so that people can't take over the drone, but that we don't need to encrypt the downlinks" https://www.computerworld.com/article/2522263/drone-incident-serves-up-data-encryption-lesson.html
As far as latency goes, I think you're wildly overestimating the impact of encryption. E.g. look at an SSD that supports hardware disk encryption (like most Samsung drives). Total access latency, including encryption or decryption by the SSD controller, is tens of microseconds. Meanwhile, these drones are potentially being controlled from thousands of miles away (e.g. the pilot is at the Creech AF base in Nevada, flying a drone over the middle east), meaning there will be tens of milliseconds worth of latency at a minimum based on the laws of physics alone (nevermind how much time it takes in reality for a signal to be relayed by a bunch of satellites).
As far how Iran downed that drone, I don't know. The fact that the control link is encrypted doesn't mean it's impossible to compromise the drone in one way or another.
That's really not the same, as GPS data doesn't come from the ground control station, it's not part of the control link between the pilot and the drone. And the reason basic GPS isn't encrypted is so that everyone can use it, as it's hugely useful for civilians as well. Although there is an encrypted portion containing higher precision data, for use by US military and allies.
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