They don’t have the navy for it. They’re also bordered by the First Island Chain, a string of countries they have been pissing off for a thousand years.
Patrolling shipping lanes is a peacetime operation, so I don't see how the First Island Chain matters. They're not going to halt Chinese naval ships going on patrol missions. It just means the patrols won't be secret.
Patrolling shipping lanes is a power projection, one that US allies and non-allies alike enjoyed or tolerated due to the demonstration of the US’s impartiality and commitment to free trade. China projecting such power will not be seen as impartial, especially given the never-resolved territorial disputes in the region.
In ten years China’s population decline will go from “moderate” to “accelerating,” and we will be a decade into the collapse of globalization. It’s doubtful they will have the expertise or even raw materials to float a navy capable of even regional patrol, much less world patrol.
