A threat to your safety or your freedom needs to be dealt with directly by eliminating it, not hiding from it. If you're envisioning a bad actor with the resources to compile and analyze a comprehensive log of your location, the simple fact that you use service A instead of service B is not going to do a thing to stop them if they're out to get you. You have far bigger problems on your hands.
"Potential threat" is an unbounded set. If you're going to guard against every potential threat you will not be able to spend your time doing anything else.
I asked because I was curious about what sorts of unique threats are presented by, for example, a database of location data. So far I haven't seen any that aren't already present via far simpler means.
If you have a cell phone, it is constantly pinging nearby cell towers. If it has wifi, it is pinging nearby wireless networks. That information is out there, waiting to be collected. If you want to go without the benefits of a cell phone to avoid whatever threat is posed by somebody knowing where you were at some point in time, go for it. I think it's a waste of time.
I think there has been some confusion here. When I said that "The point is not that the world will end if we give away our location data, only that doing so has a non-zero cost" what I meant was that the point is not that the world will end if we give away our location data, only that doing so has a non-zero cost.
Cell phones are like cars, they are very useful but also have their downsides (cell phones reduce privacy, cars kill people). I have a cell phone and a car because I made a decision that the cost was worth the benefit. I did not need to delude myself into thinking there was no cost nor did I need to pretend that the cost was inevitable.