I have to disagree as to which country is the greater "prize". Although Taiwan is a concern, for Europe it is a secondary one. Europe has had to finally "muscle up" against Russia, as the immediate problem is the Russian proximity and threat to the rest of Europe, especially if the Russian invasion of Ukraine became successful.
The more responsibility that Europeans can take on within their own continent, then the more free the US can be in the Pacific, to try to deflect any threats there, hopefully by leading and assisting these "island chains" to defend themselves.