For me, i would always keep her beside me for below reasons:-

1. Her AOE heal will miss most of the range dps and myself if she is placed with the tank.
2. In boss/primal fight with 'push' mechanism, she will get displaced and will stay there until further instruction which is very annoying to control.
3. As a tank healer, myself is more than enough, i would want her to focus on DPS/other healer instead.
4. Constant move doesn't mean you are moving all the time, when you stop, she will immediately 'scan' her surrounding for someone to heal, when she is casting her heal, you moving doesn't cancel anything. I could not imagine any fight that requires you to keep running.