1.) Your theory assumes that the cost difference at the hospital goes toward innovation. It ignores role of public money that goes into research. It is also not analyzing where the money are actually going.

2.) With this theory, if it is true, you are basically volunteering American patients to pay for innovation worldwide. That is quite a bad deal for quite a lot of American people.

3.)

> My speculation is that the rich people you refer to are more likely to be trained in economics (formally or otherwise) and are more likely to have a long term mindset regarding cost benefit tradeoffs.

They have also different interests. Good cost benefit tradeoffs for one group is often very bad deal for another group.