I think that's the point - Europe has far less of a concept of beer "styles", beer is not something you get out of a book but a statement of identity that can't be divorced from its history and geography. Americans aren't rooted in the same way. Compare how US sports teams are franchises to move from city to city whereas European teams are named simply Liverpool FC or FC Barcelona. They are forever tied to a particular geography which in turn ties them to the history of their region and its cultural identity. You can't buy that - but people who use the name are trying to profit from that history.
Sure, there's an element in which the people of Cologne are trying to build a "brand" like the Trappists have - partly for commercial reasons but also for quality reasons. You may feel that you're honouring them by your attempt to copy their beer, but they feel like you (or at least commercial producers) are trying to pass off a poor imitation in their name. Do you think Rolex feel honoured by all the people selling "Rolexes" in Hong Kong?
Compare Scotch ale and Scotch whisky. The US interpretation of Scotch ale resembles
the original even less than IPA or English muffins, it's complete nonsense. In contrast, Scotch whisky is a textbook example of protecting their brand - you are in no doubt that it comes from Scotland. What's more, by preventing foreign whiskies calling themselves "Scotch", it's done other areas a favour in the long term by giving them the confidence to develop their own identity as Irish, Japanese, bourbon etc. There seems to be something similar happening with lambic at the moment, the US producers being forced to make that leap from clones to being a thing in their own right.
So no, kolsch isn't a "style".