[jltsiren]

Modern cities have a lot of buildings that are sparsely populated. 500 years ago, major Italian cities had ~15k people / square km, which is similar to Brooklyn. Paris had 35k to 50k people / square km, making it more densely populated than Manhattan.

2000 years ago, Rome had similar population density to Paris 500 years ago.

Historically, urban people wanted to live inside city walls, if possible. When the population grew, most of the growth turned into higher density inside the walls. There was always some urban sprawl outside the walls, but that was mostly poor people and those who didn't have the right to live in the city proper. Major cities occasionally built a new set of walls surrounding a wider area, but that didn't happen every century.