Actually that would be the same concern of the US Treasury. The US population can accept a new bill. But there are many countries (Oil producing countries) on whose acceptance of the dollar and US currency we don't want to jeopardize.
Hence why the old currency would continue to circulate internationally.
If not being able to exchange that old currency with the new US domestic currency (except at borders and banks) and that helps track drug profiteers, so be it. But if the exchange rate is not one to one, how does it get set and that would seem to lead to problems.
But US bills in commerce internationally, isolated from US commerce domestically except by customs exchange (ostensibly) will lead to each currency having a different value because they no longer flow freely among those two different markets.