I generally disagree with everything else you’re saying but something that hasn’t been called out is that The Indies was never used to refer to India, the country. In current day, there’s the West Indies, which are annoyingly next to North America. In the past, East Indies or ‘The Indies’ referred to the greater Indian peninsula, but not the country itself, and not West Indies. By using this example, you’ve highlighted a flaw in your argument that the term ‘America’ has to encapsulate North America and South America, as ‘The Indies’ doesn’t even encapsulate West Indies.