Final answer:
The disbanding of American legislatures meant colonists had no say in lawmaking, leading to the protest against 'taxation without representation' and exacerbating tensions from the imposition of the Quartering Act. This infringement on colonists' rights escalated the push towards the American Revolution.
Step-by-step explanation:
The impact of the disbanding of American legislatures on the American colonies was significant as it removed their say in the creation of laws. Without their local assemblies, colonists lacked direct representation, which was a foundational element of their rights as British subjects. This absence of representation led to widespread protests, as colonists believed only their elected representatives had the legitimate authority to levy taxes and create laws that affected them. This concept was deeply rooted in the principles of the Magna Carta and the English Bill of Rights. Taxation without representation was a core grievance that fueled the coming of the American Revolution. The Quartering Act further exacerbated the situation by imposing the cost and burden of housing British troops onto the colonists, without their consent.
The disbanding of legislatures directly conflicted with the traditions of self-rule and salutary neglect that the colonists had enjoyed for over a century. Being accustomed to a degree of autonomy, the loss of their legislative assemblies was more than just a political inconvenience; it was a direct challenge to their liberties and way of life.