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This means you couldn't non-string values on DOM interfaces, and that includes methods, so most of the DOM's functionality goes out the window.

Good point, but HTML already has a workaround by using strings:

Now, I'm not a JS developer, so my opinion shouldn't count for much, but that looks like a much less usable standard to me.

Yeah, that works, but it requires func() to be on the global scope. It doesn't scale as a solution.

Does that matter now that we've got (possibly declarative) shadow roots as the units of DOM encapsulation?

Yes, even more so. You end up with encapsulated DOM without encapsulated script.