Singapore does exactly that, and they explicitly warn outbound Singaporean travelers that any drug use outside Singapore will be prosecuted as if it has happened in Singapore.
They're warning everybody, not just Singaporeans. It's just that Singaporeans are the most likely to go travel abroad, have some fun, and then come back like nothing has happened. But if somebody inbound gets caught in a random drug test at the airport (they do that), he's going to be prosecuted just the same no matter their citizenship. There were several (in-)famous examples of this happening.
