I thought that each city had specific rules about those sort of permits and such. I don't know what the rules are in New York. While the protesters may be willing to risk injury, the City may not be willing to do so. On the surface, it does sound unfair, but they judge may have good reasons for the decision. You are still getting to hold your protest, just not in the way you originally wanted.

Remember that a large protest could be a target for a terrorist attack.