At one point, the Papacy would have insisted that you had it backwards: The Pope is the vicar of Christ on earth who anoints the Christian world’s monarchs. You should ask why temporal rulers do not always acknowledge or attempt to work around the Pope’s infallible supremacy and authority.

Sovereignty and politics is a strange thing, in that we need to be careful not to project our notions of statehood into a past when these notions weren’t as universal as they might be nowadays. This is particularly true for medieval Italy, which was locked into a sort of unspoken “Imperial Logic Trap” (my words, not really anyone else’s) in understanding where authority originated: was it with the Pope? Was it with the Emperor? Who was the Emperor? Italian political thinkers (and various politicians) offered different answers at different times. Suffice it to say that starting from Otto's coronation, the Papacy's insistence on anointing an "Emperor" (a practice beginning with Charlemagne, but really enshrining itself with the Ottonians) eliminated the legal or social space for a ruler to claim the right to rule Italy, least of all the Pope who crowned that very Emperor. I touch upon that in moe detail in this older answer examining why Italy didn't unity until the 19th century.

But the Papacy undoubtedly exerted some temporal power. Did the “Papal State(s)” in Central Italy represent an area of direct temporal control by the Pope, or was it a particularly successful establishment of a geographic power projection by the city of Rome and its Bishop (who just happened to be the Pope)? Why can’t it be both? This means it would represent a possible (and common) path in Italian state building as well as representing exercise of authority as the Papacy would expect to exert in a perfect world (without pesky local institutions getting in the way).

How different was this from other Italian cities? While in most Italian cities, the balance of authority migrated away from religious authorities (urban bishops) and towards secular authorities (urban councils) in Rome the opposite migration occurred. Thus while the Italian cities like Florence or Milan expanded their area of control by securing the submission of other councils, the Papacy’s temporal authority was instead expanded by reaffirming control by religious authorities. Where strong secular authorities countered this expansion of religious authority, a barrier to the Papal State’s expansion appeared.

This ultimately means the the Papacy was subject to the same limitations that other Italian States were subject to when constructing a large state, and these same forces hampered constructing a state that might envelop the entire peninsula.

You might also be interested in this older answer of mine on what the Papal State was really, which might offer a bit more color on how the Papal States were different from political actors in the rest of Italy, but also in some ways not that different at all.