Growing up in the NYC area I saw many 4 to 6 story apartments, built mostly before elevators became common and practical. The upper floors were considered undesirable due to all the stairs.
Edinburgh had residential buildings up to 14 or 15 stories in the 17th century - land inside the city wall was very limited and building outside the wall was unpopular due to the threat from England.
Although due to the geology of the place you can "cheat" this by building up a hill, it's not quite the same as building a freestanding 15 storey building. There are several places I know round the Bridges that have street level entrances four floors apart.
For ancient urban dwellers, though, you’d have to weigh the inconvenience of climbing stairs against the inconvenience of walking miles in from some notional suburb. Certainly in the case of Rome, there was really no option for most people.
Eight stories seems like quite a lot.