Why did traditional Chinese city gates include a second, inner walled courtyard?

Answer: To trap attackers in a kill-box if the outer gate falls

To trap attackers in a kill-box if the outer gate falls ✓ — Correct! The 瓮城 (wèngchéng, 'urn city') is a small enclosed courtyard between an outer gate and an inner gate. If attackers smash through the outer gate, they enter the urn — and the inner gate stays shut. Defenders shoot down from all four walls. Nanjing's Zhonghua Gate has THREE such urns stacked, plus 27 hidden chambers for soldiers — the most complex surviving city gate on Earth.

To inspect tax cargo before letting it into the city — Wrong. Tax inspection happened at the outer gate or at dedicated customs stations, not in a fortified kill-box. The urn-city's design is purely military — too small and too lethal to be a customs office.

To park merchant caravans overnight outside the city — Wrong. Caravans camped at dedicated caravanserais outside the wall. Trapping a caravan in the urn-city would block the gate. The space exists to kill people who broke in, not to host people who didn't.