You do realize Imperial City in the Classical era of Athens, Sparta or Rome and “Imperial City” in the medieval period mean two completely different things, right? Even Venice had relatively little interest in conquering other cities – what they wanted to do was secure their trade routes and supply lines. Imperial or Royal cities in Central Europe just meant they had Imperial immediacy, meaning no prince had any authority over them except the Emperor or King, and in the case of the HRE, that basically meant Laissez Faire.
I don’t think it actually is an open question at all. It’s a recognizable process. Jurg Gassmann and I found a bunch of records a few years ago which described the process in Bologna – regulations for their Armed Societies in the years between mid 12th century through the early 13th. I believed he published something on it though the emphasis was on the use of urban cavalry in the militia not so much on individual citizens rights, but they were also in those records.
It was simply a matter of when the larger part of the population, usually meaning the artisans, became a substantial part of the city government. In most places this took place in roughly that same time period, in some a little earlier, in others a bit later. For example in Flanders the biggest changes took place after the big victory at the Battle of Courtrai in 1302. The craft artisans played a major role in the war so they demanded great rights in the town government.
Most towns went through a phase where they became independent, usually ruled by their merchant class or so-called ‘patriciains’, then they went through a second phase where the artisans other middle or working class estates took some power in the government, typically in the high medieval period.
By the late medieval period, towns which still had autonomy, mostly in Central and Northern Europe, had some kind of mixed or hybrid government which involved some representation by the crafts and some by the patricians and wealthier merchants.
For example Strasbourg had a Senate consisting of 300 craft alderman, a council of thirteen (for defense) a council of fifteen (for finance) and a council of twenty (for guild laws). The first two were split between craftsmen and patricians, the last was patrician only. It was a shared power arrangement which was agreed to after the craftsmen had won a series of successful uprisings.
Most towns with an artisan or partially artisan government had pretty liberal weapon laws for citizens. Again, this is because the citizens made up the bulk of the town watch and the militia. That’s the difference between north and south of the Alps. The Italian towns were getting worn out by war and invasions and gradually gave over control of their militias to military contractors, who eventually took over, ala the Sforza and Visconti in Milan.
In France and England the monarchies were much stronger, and the same eventually became the case in the Iberian kingdoms. But all of the dynamism in the High to Late medieval period was in North-Italy, Flanders and the Holy Roman Empire in roughly that order. You really don’t see that much great art or literature coming out of France or England compared to the more urbanized regions of Europe in this period. Their heyday was later, with the opening of the Atlantic in the Early Modern Period.
