That’s a bad idea. First you need to understand that for the government to be able to track every citizen first they must be able to track every phone, and then be able to figure out whose phone is who. You’re trying to break their tracking by denying the second step but in doing so you’ve made yourself a priority target.

Imagine you’re a government trying to track all of your citizens, and you’ve got the GPS data for every phone, and now need to assign them to specific persons and/or decide who you track specifically. Random Joe who goes from home to work and work to home will be last on the list, but a person whose itinerary changes every week, and drastically changes after a couple of months is someone that sticks out. And the moment someone notices this, it won’t be difficult to track other users with the same behavior, and realize they’re switching phones by comparing one phone’s behavior during one week to another phone during another week. And now they have the same information they would before, except they have their eyes on you more closely.

Plus you would probably need to login to your email or some account on the phone, and that would be enough to track that you changed your phone.

The best idea to avoid this sort of surveillance is to only carry your phone from home to work and back. No one will bat an eye about someone going for a run or something without his phone, and from someone tracking you’re just a boring person who only works and goes home.