Yes, that is an idea. I mean, many things on this world doesn't depend on what is reasonable and what is not. But, if local trademarks are considered in that case, than why somebody would care about the American trademarks. If not, than it would be fair for american compaines to respect other countries trademarks. But in that case, what if there's, for example, McDonalds as a local trademark in some other country, and is older than american and quite popular in its country? Would it be fair that McDonalds close their site? Off course, maybe this is not possible for McDonalds, but for some other name, why not?
This seems quite complicate...