"Banana republic" implies more than what the dictionary definition is. If you look at the wealth distribution in any example "banana republic", you'll find a few very wealthy people/warlords and many dirt poor with close to nothing in between
There’s already a well-established word for a country run by rich elite.
Calling the US a “banana republic” is a shocking headline, which I think is the real point. The US economy is not very similar to actual banana republics though. There are some aspects which are becoming similar, yes, but also many in which they’re not.