That's not it works, people don't just go collect someone wanted who is arrested in a country with an extradition treaty

It can take years to go through the motions of multiple appeals, take Julian Assange in the UK for example

I understand where you're coming from. But, in reality the prosecution has wide latitude within the justice system for sealed indictments, warrants etc. Extradition can be expensive and time consuming even if there is an agreement with another country it might years before the person is extradited. Just look at example of Kimdotcom, he is fighting his extradition from NewZealand for 10 years and popping out half a dozen babies.