Interesting that this was just about spying, when the real reason to keep work email off your phone (imo) is to maintain work life balance. If I can access my work email on my phone, I will access my work email on my phone. Constantly. I'm bad enough with my phone and my personal email.
Everywhere I've worked I've told my manager I turn off work when I leave (unless I'm oncall). I've never had this be a concern, across three large companies.