Because apps aren't allowed to be persistently running in the background. So you'd have to get the user to actively open the app while using the toothbrush which is annoying. If you let it connect to wifi, it will just work always without any manual user effort.
They are allowed to run at intervals. Just make the interval short and control it by the GPS location so that it doesn't ping the brush when you aren't at home.
Really? Why not?