Question

why did each of the states write a constitution as soon as independence was declared?

they were required by the british government to create them.

they needed to replace the british government after the war with their own government.

they needed a way to force colonists to join the war effort.

they believed that a monarch would take over if they waited.

Explanation:

After declaring independence from Britain, the states needed to establish their own governance structures. A constitution would define how their new governments would operate. The British government would not require them to create constitutions as they were now independent. Forcing colonists to join the war effort was not the main reason for writing constitutions at this point (the war was related to independence, but post - independence the focus was on governance). There was no real threat of a monarch taking over. The most logical reason is that they needed to replace the British - imposed governance with their own, which a constitution would help structure.

Answer:

They needed to replace the British government after the war with their own government.