Why Isn't the United States Trying to Free the Commonwealth Realm(s) From the United Kingdom?

 Now officially the US stance on Taiwan is, "The United States approach to Taiwan has remained consistent across decades and administrations.  The United States has a longstanding one China policy, which is guided by the Taiwan Relations Act, the three U.S.-China Joint Communiques, and the Six Assurances.  We oppose any unilateral changes to the status quo from either side; we do not support Taiwan independence; and we expect cross-Strait differences to be resolved by peaceful means. We continue to have an abiding interest in peace and stability across the Taiwan Strait.  Consistent with the Taiwan Relations Act, the United States makes available defense articles and services as necessary to enable Taiwan to maintain a sufficient self-defense capability -– and maintains our capacity to resist any resort to force or other forms of coercion that would jeopardize the security, or the social or economic system, of Taiwan." Sounds a bit weird to say the "one China policy" is "longstanding" in the beginning only to end with "the United States makes available defense articles and services as necessary to enable Taiwan to maintain a sufficient self-defense capability," (especially if you translate "articles and services" to be "weapons and troops") because such actions may be to the detriment of a one China.

We can see it in our media as well: at best the US relationship with Taiwan is a question mark and it's relationship with China is border-line hostile. 

Listening to the more militaristic American leaders, China is a bully threatening to dominate Taiwan and take it's resources. 

But here's a question: if the US is so concerned with sovereign states being controlled in a quasi-authoritarian way, why are they ignoring United Kingdom?

See, United Kingdom has some called the Commonwealth Realm (not to be confused with the Commonwealth of Nations). The Commonwealth Realm is currently 15 sovereign states under the rule of the monarch of England. While the relationship is up for debate (sound familiar?)  with interpretations ranging from, "the King/Queen of Great Britain is also the King/Queen of Canada" to "the non-British realms are 'derivative, if not subordinate' to the crown," the average person probably doesn't think Jamaica or Australia is beholden to the whims of King Charles. England never exactly had the geology required for the resources needed to support itself long-term, which explains, well, colonization. 

Now, before anyone responds saying that China has a more obvious authoritarian government, please note that even Wikipedia describes China as a "Unitary Marxist-Leninist one-party socialist republic" while calling the United Kingdom as a "Unitary parliamentary constitutional monarchy." If we were to focus on only the noun used for describing both nations, which seems more likely to lord over its people: the "republic" or the "monarchy?"

In the end, this is about hegemony, and if the United States were being honest they would  focus on countries that truly exemplify that. But of course, sending weapons and/or troops to the Bahamas or New Zealand to fight for independence from the British is silly, right?