It's about separation of concerns. Who defines what is the same and what is not? It's computers, so you need to be clear about this. You can't emulate our judicial process, here: make a law with a spirit and define the corner cases as they get litigated.

You already mention this yourself: you don't want the browsers to "do something about it." Ok, but somebody has to. So, if not the browsers, then ICANN. But they would be using the very same algorithm, in the end, no? If so, then why not have the browsers do that, in the first place? They have more control over UI, and it is a cleaner separation of concerns and responsibility.

Somebody needs to do something. And because this is about humans (in the end, when you say "similar looking", you mean "... to humans"), better have that be in the part of the system that actually is about them: the user agent. ICANN is too slow to be able to rapidly adapt to changes in this fight.