Not a good idea to leave the power cable plugged in and switched on
whilst working inside a system. That low standby voltage isn't a
danger to the user but it sure is bad news for components such as
memory sticks and PCI/AGP/PCIe cards. Removing / fitting any parts
with voltage still present ( even residual voltage after unplugging )
can lead to damage - memory sticks being particularly vulnerable.

Anti-static straps are good as far as they go - but the danger is that
the crocodile clip comes adrift unnoticed and you think you are safe
when you are not. Personally I prefer to work bare-armed and keep in
contact with the case - it also helps working on a wooden floor and
also not wearing synthetic fibre clothing.