I guess we're interpreting the same sources differently - the English city carry law you quote allows for a lot of exceptions (eg anyone entering or leaving the city - which would cover most adventurers), and in the later Roman empire pretty much every non-slave permanent inhabitant was a citizen.
Even today in England, which has some of the most repressive laws in all human history, I've just been out and about this morning with a 4' staff of chestnut wood that could give anyone a good crack - entirely legal since it's my 'walking staff'.
The video presenter explicitly explains 2 minutes in that 90% of the people of a city were effectively disarmed by this law. Then he explains how the exceptions you noted really do not swallow the rule.
The section about the "entering and leaving" the city is at 3:30-
upon entering the city, you were directed by city guards* to store your weapons in your place of lodging and would be permitted to carry that far, but no farther.
And by carry, it is highly possible that the law meant just that- remove the weapons from their ready storage on the hip, back or what have you, and carry/transport them like your other possessions. (This IS speculation on my part, but based on his "90%" figure.)
Travelers (our adventurers) who were in temporary housing would be forced to leave bigger weapons in the care of the innkeeper, whose legal duty was to store & safeguard those weapons. Only upon leaving that lodging for another place were the weapons to be returned.
If my prior speculation was correct, that meant you could carry your weapons as a possession, but not wear them at the ready, until you were at the city boundaries, ready to leave. If you were merely changing lodgings within the city, you could not legally kit up on your travels between the two locations.
* many of whom were probably former adventurers with knee injuries from arrows.