An "unwritten" US constitution

I got to thinking the other day about the divergence between American and British norms of governance, and it occurred to me to think of what effect a sort of British style "unwritten" Constitution (in as much as the traditions of government are based on precedence and custom, with some major documents that stick out, like the Magna Carta or the English Bill of Rights) might have on American political development.

Fundamentally, the US Constitution that was ratified in 1787 was a mirror image of the British norms of government of the day, idealized and transferred to a republican setting. The president was given the powers and responsibilities very similar to the King of Great Britain, but restrained so that he would act as the King ought to have acted in the Founder's mind.

So what would preventing American constitutionalism from crystalizing do to American political history? Could it be achieved simply by the government under the Articles of Confederation adopting ad hoc solutions to it's political issues without a formally drafted replacement?
 
Have the transition to independance not be a revolutionairy struggle, but instead a slow process of reform; thus the idea of tradition and if it ain't broke don't fix it play a larger role in the US constitution.

Note that the UK constitution is based on Parliamentary soverignty, so you would also need Americans to be less scared of government.
 
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