Except it wouldn't. Modern Canada has been influenced a lot by the success of the American experiment with constitutional republicanism. If the American Revolution had failed, Canada would be a very different place (exactly how is hard to say). Same with Britain. It has also been influenced tremendously by the political experience of this country. While I doubt it would be the fascist state portrayed in that Sliders episode, it might be less democratic than the modern UK.
Those reflections on that stupid episode was what I thought of when I read Dylan Matthews' list of "3 reasons the American Revolution was a mistake." Even if you believe that the British parliamentary system is better than the American system, I doubt that the British system would be the same if the American Revolution had not happened.
Counterfactuals are hard because influences go in all different directions. If the American south never left the British empire and thus there were a larger more economically influential constituency for slavery in Britain, would Britain have abolished slavery as soon as it did? If Britain held on to its more densely settled North American colonies south of the 45th parallel, would it have been as kind to Native Americans? I have no idea, and neither does Dylan Matthews.