I think you had better look at the facts of history. Rome had been sacked by the Germans under the Emperor Charles and the pope was in no position politically to declare the Emperor’s first cousin, the princess Mary a bastard. Also, the Sultan,, the greatest power of the age, was banging at the doors of Vienna, and both the Pope and the Emperor had even worse things to worry about than an English schism. As to the Medici, things, the petty politics of Renaissance Italy, mattered not at all after 1526, with that sack of Rome.
Hmmm. I don’t think I made any comment on the power of the pope to declare Mary a bastard, annul the marriage or anything else to do with the power struggles including those involving Charles or Hapsburgs. Whether or not the politics of the Renaissance were petty or not is a matter of opinion.
I merely noted that the Pope, and the Medicis did hold religious and political power just as the monarchs of Europe and he was a power player, although not always successful. He obviously had enough power to put caution into Henry’s mind and induce him to take threatening actions to pressure as well as persuade the pope to accede to his wishes. Clement feared the wrath of Charles V and refused to annul the marriage, leading to Henry’s excommunication and the scism.
The political and military power of the pope, the various monarchs, as well as the various city-states and ruling families like the Medicis did matter in the politics and the shape of Europe at the time.