What are the advantages of constitutional assembly?
I assume you are asking about the benefits of the United States Constitutional right to freedom of peaceful assembly ("the right of the people peaceably to assemble, and to petition the Government for a redress of grievances") which was added in the First Amendment.
This basically means that, as long as US citizens are not breaking any laws (trespassing, inciting violence or riot, etc.), they can get together to discuss and promote their ideas. This right gives US citizens a means to spread their ideas to others and to bring to light unjust and unfair practices. Protests, parades, marches and strike picket lines are all classic examples of this right in action.
Many laws and changes to government and corporate policy have been made as a result of this right. Child Labor Laws, Civil Rights Laws, Labor Unions, Abortion Laws (both pro and anti), might not exist without events protected under this right.