Why should Zakat be given locally?

It is by the consensus of all four schools of thoughts that it should be given locally. This is determined by the following Hadith:

Abdullah Ibn’ Abbas (May Allah be pleased with him) narrates: “The Prophet sent Mu’adh to Yemen and said, ‘Invite the people to testify that none has the right to be worshipped but Allah and I am Allah’s Messenger, and if they obey you to do so, then teach them that Allah has enjoined on them five prayers in every day and night (in twenty-four hours), and if they obey you to do so, then teach them that Allah has made it obligatory for them to pay the Zakat from their property and it is to be taken from the wealthy among them and given to the poor.” (Sahih Al-Bukhari)