Well, just because we have the right to assemble doesn't mean we have the right to cause public disturbances. Unplanned and unapproved demonstrations are generally allowed, but they need to walk a fine line between demonstration and mass riot. For example, I could go grab a bunch of people and make a picket line on public property as long as we did not disturb the peace (i.e. break other laws in the process). For example, if some guy complained about the protest offending him or hurting his ears, it could be broken up. However, by getting written permission, said demonstrations get more leeway and probably won't have to worry about getting in any trouble.

Pending state/city laws, the government doesn't need to approve assembly, but getting their consent usually makes the demonstration go smoother.

At least as far as I know.