Often this appeals to a traffic management justification. The transportation rationale implicitly prioritizes the movement of people cutting through the area in cars over anybody using the sidewalk, who becomes trapped on the overcrowded sidewalks. It sets the privileged minority who own cars in New York City above the majority who live car-free. It does also keep the roadways open for emergency vehicles to get through quickly.
Rapid responses may be critical to provide medical assistance for anybody who may be injured by a confrontation or stampeding from the crowd. It also allows the police to mobilize their own resources, enabling them to respond with overwhelming force, both in terms of bodies and weaponry.
Former Mayor Giuliani once expressed this rather concisely:NYPD are keeping people on the sidewalk #GeorgeFloydProtest pic.twitter.com/uDSuCYhe9M— Andrew Solender (@AndrewSolender) May 29, 2020
I have a zero tolerance for riots. I, you know, took over a city that had two riots in four years and I had none. And they knew they couldn’t riot on me. And when I saw the people on the street in New York City, I said to myself, you’re breaking Giuliani’s rules. You don’t take my streets. You can have my sidewalks, but you don’t take my streets, because ambulances have to get through there, fire trucks have to get through there. People die when you crowd the streets of New York City with protesters. You can do plenty of protesting on the sidewalk.As the statement by Giuliani shows, there is a hierarchy here between the "streets" and the "sidewalks." There is also a power of ownership ("my streets") at work here, and the protesters are merely allowed use of the lower status portion of the public space by those in power.