The idea of running out of things to do in Rome, Florence or Naples in 12 days is a little difficult for me to believe.
Nobody said this of course. The OP expressly sought opinions on how to best shape an initial 12-day trip to Rome, primarily, but one that might include Florence and/or Naples. So opinions could range from 12-0-0, to maybe 8-4-0, and conceivably an even split 4-4-4.
No opinion is right or wrong, but it has become something of a cliche on here, in just about every itinerary thread, to say things like "You could spend a lifetime in Italy and not see everything ..." or "We've spent weeks in XXX and we still haven't seen everything ..." - and many similar sentiments.
Some people go to an even stronger version of this meme ... "You have to spent X nights in YYY" (or it's almost not worth going, or you're a hopeless box-ticker to see it in less, and so on). With the greatest respect, all of this is often irrelevant, and not helpful.
How many days out of twelve in Rome ... that is the issue the OP wants a view on; the city might have 600 worthy churches, but it hardly matters. And I don't think it can justify the 12-0-0 extreme option.
And if an OP wants to "feel like a Roman" by sipping coffee, buying groceries, and indulging in gelato, I think it's worth pointing out (a) the diminishing marginal utility of each additional day doing that, and (b) the opportunity cost of "missing out" on other good stuff just a couple of hours distant.