Kind of off-topic but perhaps you will find it useful:
I agree with the first part of your response but not the second. Yes, China should keep strengthening its position and not launch a war unless absolutely necessary for the foreseeable future, but while that might get it Taiwan it won't break the US's APAC hegemony. Can you point to a single example in history where a hegemony was broken without a war or the hegemonic state imploding due to internal factors? In other words, a hegemony that passed without a war and with the hegemonic state still intact and functional.
This is misunderstanding of terms that reminds me of "
America is not a democracy but a republic" except that Greek for "Hellenic Republic" is Ελληνική Δημοκρατία (Elliniki Dimokratia).
Languages are evolved structures that facilitate communication so the meaning of the word should be understood through interpretation of the meaning in its natural context (linguistic
ethology) as deriving meaning from etymology alone can be misleading. I think this should be particularly obvious to people who speak both Chinese and English and often are challenged by translation.
If we apply this to "hegemony" we find that the Greek word
ἡγεμών (ygemon) literally translates to "leader" but its proper meaning should be derived through an analogous Latin term
imperator.
Imperator is a title bestowed by the Senate on the military leader in charge of one or more legions.
Imperium was the title of authority bestowed and it referred to power over free men, as power over things and slaves was called
dominium. Imperator was the ruler of men, dominus was the ruler of things and slaves.
Similarly the title of
ygemon is bestowed by
polis (Greek city-state ) on the military leader in charge of the polis' military which then would be either referred collectively as a "ygemonia" or divided into multiple units called "yegemonia" each with its "ygemon". This naming convention lead to the creation of a separate title of
strategos which referred to the supreme commander of forces from multiple poleis during the Persian wars, since to refer to such person as "hegemon" would imply direct authority over the militaries of sovereign city-states. The title of "hegemon" was used to describe the city-states of Sparta, Athens and Thebes who held a similar power over other city states as an ygemon held over his soldiers.
So whenever you are referring to "hegemony" of the United States you are
literally referring to an
empire which is a very specific thing.
An empire is a structure in which one state is capable of violating another state's monopoly of force without entering a state of legal war. So for example any protectorate is an empire because withdrawal of military protection a legal threat. The protector doesn't have to threaten the protected directly for the threat to take effect. A subject state in an empire is sovereign in all matters except any intervention by the imperial power.
Therefore it is impossible for an empire to continue existing and cease to exist at the same time. It is possible for one state to push out another state's imperial power from a region, but not to "break it". If the empire continues to exist then it can return to the region - as it was the case of many imperial provinces changing hands between empires throughout history - as soon as the power that pushed it out initially weakens sufficiently. However to "break" an empire means to "end an empire".
So the question you should ask instead is "
if US power is pushed out of West Pacific can the US continue as an imperial entity" to which my answer would be "
extremely unlikely".
US imperial power depends on its monetary creation which sustains its power - both political and military - and that to a large extent depends on the USD demand generated by WestPac region. Currently China, HongKong, Taiwan, Japan, South Korea and Singapore account for approximately 6 trillion USD in reserves which is more than the rest of the world combined.
So while it is theoretically possible for China to take over the "hegemony" in the region while allowing USD to function as reserve currency it would effectively put the US under Chinese control so the US would resort to war or deliberate destruction of those reserves through economic means. If there's one factor that is always inextricably linked with political power it is means of debt repayment and with the US having no economic leverage over China to balance that it must use force.
Empires are inherently unsustainable and the only way that they can stabilize long-term is if they create civilizations. Once that happens they enter a process of dynastic echange like China and its imperial dynasties or Europe which recreates a binary of "Rome" and "Greece" throughout its history (currently US is the "Rome" and EU is the "Greece" while USSR was is the "Macedon"). The US hasn't created a civilization so a collapse of its empire might trigger a full collapse as in Western Rome. The US is de facto two radically different states (Union and Confederacy) since the beginning - the two just shift their territory and party allegiance.
Likewise, whoever controls those instruments on Taiwan Island, which is currently the DPP and its foreign collaborators, can define the minds of most Taiwanese public.
This is inversion of the relationship between the sides.
Those two countries are DPP's "paymasters" and the US is DPP's
de facto political sovereign. DPP is the equivalent of the communist parties in the Warsaw Pact countries - puppet-like collaborators with the occupying power. It is a tool of social control, not a venue of democratic expression.
Modern DPP was created during the late 80s internal purge of reunification supporters to shift the previous strategy under KMT of Taiwan as entry point into China's political structure toward Taiwanese independence as a credible threat of war to China. This was seen as necessary to facilitate China as additional USD buyer, along with intervention in the Middle East in the first and second Gulf War. It is all about finding dumping ground for USD following the economic resurgence of Europe and the decline and collapse of the Soviet bloc.
This of course is only a part in the broader control system as like Japan or Korea
Taiwan is not a proper democracy as any system that uses First-Past-The-Post to elect a majority of representatives is by its mathematical nature pseudodemocratic.
The proper definition of democracy is not ideological but mathematical. It's
how independent of other factors the collective decision-making process is. Democracy or "full democracy" as it is sometimes called in modern political parlance requires that
the distribution of voters' choices must be reflected in the distribution of the outcomes. FPTP forces voters to vote
against rather than vote
for as well as to include radical positions without an alternative. It's as disruptive as a single-party list.
Parallel voting used on Taiwan can be considered democratic if FPTP results are adjusted by party lists like in Germany but the system on Taiwan is essentially a modified Westminster system with majority of seats elected through FPTP and the party list electing less than half of the number of seats being a independent vote that largely mirrors FPTP results. "Democracies" of East Asian US vassals are a fraud perpetrated by an oligarchical structure and/or external power to divert attention of the controlled population from the control system - and that includes the US population thinking that they are defending "democracies".
Personally I don't think democracy - which is a product of European culture - fits with the East Asian culture. Decline of US influence will most likely mean a decline of "democracy" because while European culture is built around tribal councils and contesting of power East Asian culture is not. What we find inherent to resolving political conflict most Asian cultures find highly disruptive and in both instances it has to do with geography - what is sustainable in Europe is not sustainable in Asia... or in North America. Hence pseudodemocracies emerging in Russia or the US which are the consequence of European cultural influence clashing with geographical reality of power projection. Functional democracies are very unusual thing because they reside in a "goldilock zone" of heavily reacting elements that form a a functional if messy ecosystem. Similarly China occupies an "island of stability" as a large, heavy element. The analogy is not perfect but I hope it illustrates my point about politics culture being just physics with extra steps of carbon-based life developing sophisticated reproductive strategy called "civilization".