People are actually working on something very similar to this in research [1]. By applying random noise to location data the user's individual privacy can be protected while still allowing for collection of usage (or in this case location) statistics etc. This is the key idea behind local differential privacy (which Apple also uses to collect anonymous statistics on usage data [2]).
[1] http://www.shivakasiviswanathan.com/ICDE16b.pdf
[2] https://machinelearning.apple.com/docs/learning-with-privacy...