Well, they might try but that would just add to the chaos. Do you think folks are going to readily surrender the money? How about in countries where the government holds little sway.I have thought this through and think governments worldwide would move very quickly to seize as much of the cash as possible.
This would devalue the funds but not as much as keeping the funds in circulation might.
Now, with various governments holding the cash - the poorer countries would be able to invest in infrastructure and provide food, shelter and other basics in some places. Wealthy countries could retire all debts and invest as necessary.
I don't think you have really thought this through as a real-world problem. Your conceived solution is admirable but simplistic.