Also, nobody in their right mind would leave their computer plugged in while working on its internals.
Actually, it's not such a stupid idea, as the case is earthed when plugged in, which can help prevent damage through static discharge. I'm pretty sure my Intel SSD's leaflet actually recommended it. You're very unlikely to get an electric shock from a PSU unless you literally stick bits of metal through the grilles or open it up.
This means only the earth pin is connected, thus earthing your case but without running the risk of having live connected, even if isolated via a switch on the PSU.