I had always heard that it was a revolutionary thumb in the eye towards Britain and the monarchy, the Brits can be so anal about their 'Queen's Good English' so it makes sense. All of the misspellings that I can think of (I'm Canadian, EH?) are contractions where letters are dropped in a more utilitarian and practical manner, so that would be in keeping with the Puritanical ideologies of the Founding Fathers as well.
Most likely a little of both the cost per letter and dictionary . May I also suggest , there may be some difference due to common usage . We as Americans frequently pronounce the same words differently , than the English , and chances are in sounding out some words , we became accustomed to spelling them the way we pronounce them , rather than the way our English cousins pronounce and spell them .
A lovely theory, but to the best of my knowledge not true. I've always been told that it's all down to Noah Webster, lexicographer of the Webster Dictionary, who felt that American English should be independent of British English - thus he looked at the roots of many words and chose his own spellings - as in color, in which case he preferred the Latin root color.
This sounds less likely to me. I also think it would be a more famous thing if one person arbitrarily changed how everyone spelled. I could understand, however, if it was a combination of the two. Both make sense along with it being rare to have a complete education and "sounding out" the words was very likely. I love reading old letters and see this quite a bit.