I'm former Russian resident.
First, there are still some cases when permission for protest event is not required. It's a picketing performed by single person, for example. In this case police will pack protester in a matter of few minutes and deliver him to a police station for fake reason like "personality identification". So, legitimacy is not the thing.
Government doesn't appreciate protests, so it creates artificial barriers by means of law manipulation, and it'll always be winning in this field. All this paperwork required to approve meeting is like implicit reject, or a lever which allows to mitigate real impact of social event. Namely, it can be approved to conduct meeting on the edge of the city in time when it will be not relevant anymore.
Protests are social counterweight, which allows people to push back. The very idea that counterweight be dependent from other's side permission is just ridiculous.