The accelerometers in phones have wake-on-motion built-in. They use essentially no power when there is no motion, with a sleep/wake delay of something like 1ms.

The accelerometers in phones have wake-on-motion built-in. They use essentially no power when there is no motion, with a sleep/wake delay of something like 1ms. Even when the accelerometer is powered up, it uses negligible power compared to the CPU/display/radios. The reason you wouldn't want to use the accelerometer all the time in an app is that it keeps the CPU from sleeping, since the CPU has to be awake to read & process the signals from it. Keeping the CPU awake when it could otherwise be sleeping is going to drain battery far more than the accelerometer itself.