What deep-rooted american ideals and beliefs are found in the mythic status of western cowboys?

Those probably were freedom, independence and self-reliance. The cowboys represent brave and unflinching individuals who conquer unknown and often very dangerous new frontiers of the Wild West. They brave all the dangers with nothing but their wits and their skill with a firearm which usually is a pistol. They are free individuals in a free open space who are guided by their instincts and their morals.

Assemblies do not have written codes of laws. laws are matters for magistrates and courts, not assemblies. codes of law are things such as civil law, criminal law, and constitutional law. what assemblies have are procedures regarding debating, voting and other business they might carry out.  also note that rome had three assemblies: the assembly of the soldiers, the assembly of the tribes, and the plebeian councils.