Why do bats roost hanging upside down?

Because it costs nothing. A bat's foot tendons run in such a way that the weight of the hanging animal pulls the claws closed, and the grip locks mechanically - no muscular effort at all. Bats do not hold on; they hang, and they can stay hooked on after death, which is why dead bats are sometimes found still in place.

The real reason is take-off. Bat wings are hand-wings with long thin bones and no powerful downstroke from a standing start; most cannot generate enough lift to launch from the ground, and their legs are too spindly to run up to speed. Hanging high solves it - let go, drop, and you are flying. Roosting upside down is a launch method.

The legs are weak precisely because they have been repurposed. In most bats the same membrane that forms the wing runs down to the ankles, so the hind limbs are part of the flight surface rather than walking equipment. The exceptions prove it: vampire bats, which need to approach prey on the ground and take off again from a standing position, are unusually good at walking, running and even jumping.