The Indus basin also turned out to be the area from which Neolithic beads originated — the hand-drilled beads had been found throughout the Middle East and Central Asia, and study showed specific patterns of drilling inside the holes that apparently reveal individual workshops / craftsmen / locales. Probably settled life and urbanization had deep roots before, as you said, the IndoEuropean invasion. The cities ran things, didn’t need walls, a situation found in plenty of other places, including classical Greece, and to some extent, Mycenaean Greece; Rome had no city wall until Emperor Aurelian; Pharaonic Egyptian cities were unwalled. The places where walled cities were common were the very places that got invaded a lot, such as Canaan (e.g. Jericho).
Rome actually had the Servian Walls built in the 4th century BC, which were formidable enough to keep Hannibal out.
During the late Republic and early Empire the city outgrew these walls and eventually they were left to crumble or were dismantled. The Imperial city had no walls, as you say, till Aurelian.
In China, BTW, walls are such an integral part of the concept of city that the writing character for city is derived from that for wall.