You do realize that capacitors have a finite amount of power they can supply right? If you were running a phone off of the caps available in current production that would fit inside a phone, you might get a second of power on time at best - probably a lot less.
Go ahead, power down your phone, pull the battery and try to turn it on. It won’t work because the caps will have depleted by the time you got the battery out of your phone, probably much sooner than that.
Cap charge decay is dependent on the load, but the caps here are so small that the ability to apply enough current to run the circuits in question necessitates a battery or some other external power supply.
In order to get location you need GPS of some sort, that circuitry (a transceiver and a bunch of other things) isn’t going to be powered for any appreciable amount of time through caps alone.
In a cell phone the amount of energy stored in the power supply bypass capacitors is far to little to perform any useful transmissions. Like many other devices, internal state in CMOS circuits can persist for quite some time (like minutes) if the circuits are in a low power consuming state.