In fact, what you see on the Ponte Vecchio is only the most dramatic portion of the 1 kilometer (2/3 mile) enclosed corridor, built to connect the Pitti Palace, on the south side of the river Arno, to the Uffizi Palace on the north. The Pitti was a fancier pile of stone built by Luca Pitti, who wanted to build one more impressive than the Medici's. His family's wealth declined after his death and they were forced to sell out to the Medicis.
Today, the very wealthy have private elevators and armoured cars. Back then, it was hard to lift an armoured palanquin, and to avoid being mugged or knifed, Medici ordered up the most extravagant, grade separated private corridor ever built. Such an ostentatious, in-your-face example of occupation of the public realm for private purposes has never been matched since.