You left out convert to another currency and/or buy from someone else, like oil.
So they buy oil - what do the people that sold it to them do with those dollars?
Yes, those dollars can slosh around for a while, but eventually they either come back here or they get stored somewhere as reserve currency.
Either way is a win for us. If they come back to the US, well it helps the economy here. If they decide to store them under a mattress, we will have gotten goods in exchange for some pieces papers whose future value is not guaranteed.