It's a bit more complicated than that.

Firenze went through several waves of

1. being ruled by a certain noble family, usually with French or Papal connections

2. a rebellion happens; a new "communal" government sees other nobles and the merchant class rule together for a short period

3. one noble family rises to the top again, or the city gets reconquered by the old family

4. rinse and repeat

The development of new towers was blocked during one of those briefs interreigns, more specifically a situations where both main factions from the nobility were absent from the city, busy fighting a war among themselves in the nearby regions.

Later, when one of the factions had come back into the city and emerged as winner, they destroyed their enemies' towers. Such enemies inevitably came back stronger, retook the city, and destroyed the left-over towers. By that point, towers were clearly not enough to ensure safety (because conflicts now involved pretty large armies), so nobody tried to rebuild them.

Meanwhile, nearby San Gimignano was remote enough to not be periodically invaded, so their towers survived largely unscathed.

> Medieval society was also able to work towards a common good.

I'm not sure that they'd have thought of it quite in those terms, but yeah, restrictions on private ownership of castles, and destruction of said castles, is basically as old as castles, and these towers are, functionally, really just a special case of castles.

Makes you wonder what modern urban planning could learn from a bunch of 13th-century Italians with too many towers