Why would Quirinius require people to return to their hometown for a census?

Luke 2:

1 In those days a decree went out from Caesar Augustus that all the world should be registered.

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There was no extra-biblical evidence that Rome required people to return to their hometown for a census. Logistically, it made no sense to do so.

2 This was the first registration when Quirinius was governor of Syria. 3 And all went to be registered, each to his own town.

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Why would Quirinius require people to return to their hometown for the census?

Cambridge Bible for Schools and Colleges:

every one into his own city] This method of enrolment was a concession to Jewish prejudices. The Roman method was to enrol each person at his own place of residence.

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Jamieson-Fausset-Brown was similar: 3. went … to his own city—the city of his extraction, according to the Jewish custom, not of his abode, which was the usual Roman method.

Ellicott explained the motivation:

(3) All went to be taxed.—As a rule the practice in a Roman census was to register people in their place of residence; but this was probably modified in Palestine, in deference to the feelings of the people. After the death of Herod and the division of his kingdom, … the subjects of one tetrarchy would not have been registered as belonging to another.

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Why would Quirinius require people to return to their hometown for the census?

It was a special detail applicable to the Jewish population.