They won the war which enabled them to become a republican democracy instead of a monarchy. They freed themselves from central authority and wanted to have a democratic federal government to rule made out of people and not just nobles who claimed that they had right to rule.
Freedom of assembly allows people to gather peacefully
The theory that the threat of nuclear war is enough to prevent an attack is called: Nuclear deterrent
The theory is based on the likelihood that every nations would fear a mutual destruction when initiating attack to countries that own nuclear weapon. Even if a country emerge victorious from a nuclear war, the damage that caused by opposition's nuclear would damage the environment of the victors for decades.