The Roman method of collecting taxes was called “tax farming” and was practiced in other empires (including the British to some extent) as well. link
I’ve read estimates that for every four pieces of silver/gold collected, one made it to the empire. Matthew was a very low level provincial tax farmer (tax sharecropper? He’d have reported to somebody higher up in perhaps Jerusalem, who’d have reported to a capo in Alexandria, etc.- in some ways it was like the first multinational big money corporation.
It’s actually an ingenious system: it guaranteed the Romans that they would have X amount of money next year, which allowed them to plan their wars and buildings. It also wasn’t total avarice that caused the tax farmers to overcollect- in order to get the contract (which allowed them to use the seal and if necessary the troops of the emperor) they had to GUARANTEE that they would raise X is from their province; if they didn’t succeed, for whatever reason (including natural disaster or full scale rebellion) their neck was on the line and that’s not figuratively, so overcollecting would help insure that they could guarantee that if a drought happened next year they could still make their mark with what they’d stole… “over” taxed- the year before.
What was NOT necessary was to report to the home of your distant ancestors to pay your taxes. I never understood where that Bethlehem bit came from.