Your last line there is key: “the US would ignore all that.”
Exactly.
Asking Americans to care about the difference between Meghan, The Duchess of Sussex, and Meghan, Duchess of Sussex, is pointless. They’re not going to care because the important word of distinction to Americans is “duchess.” Americans are not going to care whether or not a definite article is placed before the word “duchess.” The fact that someone is using the word “duchess” in relation to someone is what is worthy of note.
No one in the US is going to stop Megsy going around calling herself Meghan, Duchess of Sussex. That girl will use it until she dies.