There are valid arguments to be made regarding the independence of states under the US military umbrella, but South Korea and Taiwain are pretty far down that list of what you could fairly call a true vassal state. I'd look to the Middle East for true examples of vassal states, states that exist largely due to cooperating with the US, who would otherwise simple be replaced by the CIA, with no popular or ideological base of support, weak sense of national identity, and a large (majority?) population of guest workers.

Saudi Arabia is an example. All those weapons they bought was mostly a bribe to the United States. Saudi Arabia doesn't WANT to have a strong domestic military because they know they are unpopular and, looking to Egypt, recognize they would probably be toppled by an effective and unified military.

On the other hand, you have al Ansar, starved and penniless, beating Saudi forces becauses they actually believe in what they are fighting for, whereas nobody is willing to die for the corrupt House of Saud and no piece of expensive technology is going to change that fact.

South Korea and Taiwain are both legitimate governments with strong public support and national identity, BUT South Korea did do dumb shit like send troops to support American idiocy in Vietnam, Afghanistan, and Iraq. But notably, South Korea, having had its military defenses stripped and sent to Israel, recently told Trump to fuck off with his troop requests; with the economic collapse of the US imminent and its military exposed as easily compromised, the era of the American vassal state is quickly coming to the end.

[Edit: On my path to correcting the following opinion: The argument for Ukraine, which I've heard from what are perhaps pro-Russian sources, is that it is basically a weapons platform for the West to attack Russia forever. Ukraine is basically devastasted as a nation, it's industrial base destroyed, it's people fleeing, it's crops unplanted and unharvested, yet it continues to fight. Why? Because it's not a country, it's a weapons platform for the West. But that isn't one I'm going to defend because I don't know enough about the situation, but it is plausible (as the best propaganda is).]

As for Israel, a much stronger case can be made that the US is a vassal state of Israel. This business in the Gulf was explicitly, per Little Marco, at the request of Israel, and only benefits Israel at great expense to the US. The US is a wagged dog.