the economic relationship of the steppe and sedentary invariably lead to armed conflict, unless one politically dominates the other (and it resets when one party rebels) peaceful contact cannot be permanently maintained. the walls were there for this eventuality.

smuggling absolutely had to be affected by these physical barriers and large troop presences. the amount of tax collected by redirecting that traffic legally certainly didn't pay for the wall, but that was only one function, it's saving tax revenue by preventing/slowing down whatever raiding it did, and protecting the state by controlling the military utility of chinese exports.

but the Romans and other ancient states are not actually exceptions, the roman border fortifications, that included long walls and massive forts, were commiserately bank-breaking investments that failed to completely stop infiltration, smuggling, or invasion. Iran has a 'great wall' in Gorgan on a route from the steppe to tabaristan. in the caucauses, Romans and Iranians built & mutually sponsored walls and fortifications to prevent passage from the pontic steppe. but the elephant in the room is that China lacked a consistent river border to the steppe, so they needed to fabricate more obstacles than people who could use a river like the romans. simple as.

what i think is compelling evidence bout the great wall in China is that steppe peoples that formed conquest dynasties in the north tended to use & expand it. if anyone would have a negative view of the system, you'd think it'd be people who'd just kicked its ass---yet the Liao & Jin massively invested into it.