This is actually a very good idea. And, this is also why it'll never happen.
If you have any experience dealing with euros, and with the one and two euro coins, then I would imagine that you would have a pretty good feeling about ditching the $1 dollar bill entirely; if not, then you don't know what you're missing.
One of the few really advanced and intelligent things that happened with Europe's conversion to the euro was the elimination of the paper single in favor of the one and two euro coin. When you have a handful of two euro coins, you've got money.
Will Americans be able to handle such a concept? Maybe gradually, but not at first. The problem, of course, comes from the popularity of the quarter and the fact that dollar coins have failed because they were too much like the quarter.
But, anyway--yes. Get rid of the dollar bill. Save the money. It would be a smart thing to do.