NEMA 5-20 is exactly that. It's somewhat less common, due to the fact that it implies a 20 amp supply. Most plugs and sockets use the 15 amp version.

Aussie plugs are more like NEMA 11 plugs: the prongs are angled to form two sides of a triangle.

You mean NEMA 10?[0] All I can dig up for NEMA 11 are motors.

[0] https://en.wikipedia.org/wiki/NEMA_connector#NEMA_10

You are indeed correct.

I'm not sure the order these were conceived, but it may be that there was already a plug with a similar configuration.

http://www.jmjwebsitedesign.com/cdpro/wp-content/uploads/201...

That's some panoply of configurations! It's a pity the most common configuration is the worst of them.