All praises are due to Allāh and may his blessings be upon his Prophet, peace and salutations be upon him.
When considering this and many other questions in Islamic fiqh (jurisprudence) it is imperative to consider multiple dimensions at once. Whilst it is tempting to get drawn into a specific Islamic text or ethical consideration, the faqīh (jurist) has to force himself to consider all available—often conflicting—considerations and overarching Islamic principles.
The four main schools of thought have given preference to distributing Zakat within the vicinity of where it is collected. The basis for this is the well-known instruction of the Prophet (peace and salutations be upon him) to his companion Mu’āth b. Jabal (Allāh be pleased with him), when he sent him to Yemen. He said to him that once they establish the prayer, inform them that Allāh has commanded that there is an amount of charity to be taken from their wealthy people and given to their poor people. The scholars took from the phrase “to their poor” that it should be given to the people who live in the vicinity of the wealth. They defined this to be those who live within a distance beyond which a person travelling is considered technically a Musāfir (traveler whose prayers are shortened).
However, proximity is just one consideration. All scholars agreed that if the need in an area far away is greater, it is better to give it where the need is more dire. This is a profound example of how jurists consider multiple dimensions when issuing rulings on such matters.