I'd say if you only own "ACME, Inc" in the US (UK), you only get to register acme.co.us (.co.uk). In this case, when no company owns an international ACME trademark, there should be a body that maintains acme.com as a simple text-only disambiguation page showing you links to each ACME, Inc with a description in the respective country's official language(s). I am nearly certain there is already a discussion buried at the end of some RFC about exactly this problem and proposed solutions, which weren't implemented because the good-enough solution was way cheaper than adding trademark disambiguation to the assigned names system.
