In the US, generally, you aren’t so much asking permission as giving notice that your expecting a generate a crowd, despite the phrasing. Freedoms of speech, assembly and association are still a thing.

The purpose behind it is to give emergency services a heads up to minimize obstruction of normal or emergency traffic and to provide some level of crowd control to minimize the chance of flash stampedes. Like if some idiot sets off a firework, everyone thinks it’s a gunshot and started running.

Approval is generally automatic, but failure to go through the approval process could result in your peaceful protest turning into a riot, or being declared a riot.