Why did the importance of religion decline throughout the colonies?

It didn't decline, it was set aside for more important things that had to be done for survival.

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.