While I'd like them to integrate Siri for tvOS into the Remote.app, I don't think they will for a while.
Siri for tvOS seems to function differently from Siri for iOS, in that it remembers your conversation and thus is quite a bit smarter. I don't think Apple will want to different Siri versions on your iOS device.
Furthermore I think many people would be confused by what Siri for iOS can do, versus what Siri in the Remote.app would be able to do.
Maybe in some time you'll be able to use Siri on your phone to control your Apple TV, but until then I doubt you'll see it in the remote app.