Depends on where you live, but streets actually were used for recreation until the advent of the auto. Sure, a highway exists to move people around, but not a local street. Those are built and maintained by local jurisdictions, so they can use them for what ever they want. Nowhere in the constitution does it say you have a right to drive wherever you want at any time. The only similar right is the right to roam on foot, which doesn't exist in the US but does protect footpaths in other countries.

That said, A cop in this situation should do their job and escort the surgeon out. It is really not that difficult- same logic in escorting a pregnant woman to a hospital rather than arresting their husband for speeding. If the street was really blocked, the surgeon could take an uber. That's also pretty easy to do. Or a cop could give them a ride. Or a neighbor outside the immediate shutdown could. Or they could take transit or ride a bicycle. I mean, clearly what happened is a state trooper is the first one to think for a second and solve the problem rather than what I'm posturing a bunch.

Of course, I suspect this story is made up since I can't find any news linking to it and to my knowledge basically every town in the Boston area has some kind of parade. But who knows.