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Machiavelli was a practical man
(startrek.website)
I greatly recommend Ada Palmer's "Inventing the Renaissance" if you have a lot of time, mild history literacy, and an interest in the Renaissance even passing. She talks a lot about Nick the practical statesmen who just didn't want to see Florence get repeatedly invaded, conquered, and looted.
https://press.uchicago.edu/ucp/books/book/chicago/I/bo246135916.html
I agree that ruler was the wrong word. "Renaissance Henry Kissinger" is certainly more accurate.
I disagree that his most influential move was the militia. His most influential move was the complex diplomatic network of alliances, treaties, and call backs to how great Rome was was objectively more influential since we actually still do it.
The Medici also didn't really beg daddy pope. I'm pretty sure that the pope was a Medici. I'll edit here if I'm wrong: Not a Medici, but was good friends with the two Medici Popes
He apparently wrote a lot in his correspondences how much he loved Florence and despite the torture, he did get a job writing the histories of Florence paid for by the Medici who did originally exile him.
All of that, BTW, was also in the wikipedia pages I linked.