But it is nonetheless much more expensive for him to enter this trade than for the Venetians to continue doing it, so he probably won't.
True, but remember, the reason we fear monopoly is because we fear that it will lead to exorbitantly high prices. At some point, the Venetians, if they choose to price-gouge, will make it worthwhile for the Pope to enter into this trade as a competitor, because he knows he can charge much lower prices than the Venetians to still recoup his initial investment.
The Most Serene Republic of Venice stole the secret of Greek Fire when the sacked Constantinople in the 4th Crusade. This enables their navy to fight off Ottoman ships that would otherwise stop trade. The Papal navy does not have this technology, and is unable to defeat the Ottoman navy. As a result, the Pope is unable to protect his merchant fleet from attack and cannot conduct the trade between Trebizond and Italy.
Well, in this case, the monopoly is really on the greek fire, and not any particular trade route. If the Pope was rich enough, he could employ scientists to study and attempt to either replicate the greek fire, or invent a suitable substitute. Or even invest in finding a profitable land route for trade. Remember, the good demanded here is "trade with the east" not "control of the seas"
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