I would be careful that you don't overhang the pavement otherwise you're effectively parked on it (like parking with wheels on it normally).
Would also have to agree it's dangerous and misleading for other road users as other road users can't see the edge of your car where they'd expect due to reflectors. That's why you're not allowed to park the wrong way round on a road for example, ie: headlights facing traffic.
Also why would you need to park sideways anyway? If you're doing that you're most likely taking up the space the other cars need to get out of said space. Motorbikes can do it, but they're a little smaller.