I think your confusion here, as I have pointed out before, is because you are more focused on other regions where there was more control over the citizenry.
In German speaking towns, the various factions of citizens simply did not trust anyone other than themselves to be in charge of their security. The citizens had to be armed so that the town would not be sold by someone who was not invested in it’s freedom. One of the incidents in the lecture where armed journeymen on their way for an after work beer came to the rescue of the captain of the town guard illustrates quite well why they had these laws. In the medieval world carrying arms was equated with knowing how to use them (rightly or wrongly) and being ready to protect the Stadtfrieden.
The northern Italian towns started out the same way, certainly in the era of the Lombard League and for a while after, but they were worn down by vendettas and the Guelf-Ghibelline conflicts, and rivalries between one another, and eventually gave over their security to contractors who eventually took most of them over. Venice was the exception to the rule as they had an abnormally stable government and a more cautious foreign policy.
South of Lombardy and Tuscany though (Rome and the Kingdom of Naples) things were more typically Feudal in Italy, and therefore more like France or Spain.
England of course was it’s own world. I remember reading a bit about some of the towns which were linked to the Hanse, like London, York, Boston and so on, but beyond that I really never focused on it, and that was a long time ago. My understanding is that those towns were reigned in during the 1390’s. The German Hanseatic Kontor in London (called the Steelyard) was self-administered and when the King tried to curtail their rights and rob some of them in the 1470s it lead to a war between England and just a few of the Hanse cities, which was won by the Hanse. They left them alone after that until the reign of Queen Elizabeth.