The nuanced argument that the article makes is not to standardize the currently common (bad) behavior, but rather to find a regime that will improve the scenario. One major goal is to make cyclists more predictable. Another is to recognize and clarify the distinction between cars and bikes.

This second point is very important. There are significant differences between a car and a bike. Cyclists have a much better field of view, on account of not having blind spots and being situated much higher. Cyclists are far more invested in avoiding collisions since they have more on the line. Bicycles are significantly less massive and travel at much lower speeds. Bicycles are narrower and more nimble and are therefore better able to avoid collisions in tight traffic.

Any regulatory regime that ignores the differences between these two vehicles is just as nonsensical as one that ignores the differences between a car and a pedestrian. As the article points out, you wouldn't expect a pedestrian to be required to stop at each and every stop sign.

The whole "two sets of rules" argument is not particularly compelling. You already deal with many distinct sets of rules in all sorts of contexts: besides the aforementioned difference in rules between pedestrians and cars, there are fifty states and innumerable other jurisdictions with drastically differing laws, there are rules that apply only to semis or commercial vehicles, there are different rules for highways and surface streets, etc. etc.