In reply to:

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


Of course there is a US dollar coin. when i was a child, it was the "eagle", then came the "susan b anthony" dollar coin, and now we have the "golden" dollar. there was also a gold (real gold, not just gold colored) $10 coin too, but these have been rare since before WWII.
and we have a two dollar bill-- but that is rare too-- one good reason to make a visit to one of the US Mints it to get a $2 bill. They are great presents for kids-- cheap souviners of US. My neice in Japan loved her $2 bill!