So we find it REALLY strange that there is no US dollar coin, or any two dollar piece at all (bill or coin).

Both Australia and NZ have one- and two-dollar coins, but for some bizarre reason, the Australian two-dollar coin is smaller than their one-dollar coin, and, to add to the confusion, is almost exactly the same size as the NZ one-dollar coin. Given that $1AUD =c.$1.21 NZD, it can be annoying to realise, too late, that the one dollar coin one has just inserted into a vending machine was actually worth $2.50!