HTupolev

A mechanical advantage (in the simple kinematics sense of "gearing") doesn't allow you to gain an increase in input with less output. I mean, it sort of does in the sense that your legs won't be operating inefficiently... but you still don't have any more power to work with than what your body is providing. If you gear down while keeping equal cadence, you will burn energy at a lower rate, but you will spend more time burning energy at that lower rate in order to get to a destination a given distance away.

A motor is providing power. It's pushing your bike. You're being moved by power beyond what your body is putting into the pedals. If you're providing 100W, and you engage an assist and drop your power so that you're providing 50W and the assist is providing 50W, you're burning energy at a lower rate, but you won't spend more time burning energy at that lower rate in order to get to a destination a given distance away; just as much power is being delivered to your wheel, so you aren't going any slower.