That's possible, certainly, especially considering Webster's dictionary was published in the aftermath of two major wars with Britain.
But more likely, I feel it was just an act of simplification. Just as there are people now who advocate changing English spellings to be phonetic or otherwise simplifying our spelling and grammatical rules to be more approachable, the likes of Webster probably saw all those 'u's (which are probably the differences we're most familiar with, or are most visible, despite there being
quite a long list of differences in all) and wondered, 'What the hell purpose do they serve?'
The only difference was back then, it was both easier and probably seen as less controversial to change, because English wasn't the global juggernaut of a language it is today, and while Johnson's dictionary was undoubtedly popular, spelling variations didn't magically disappear in the wake of its publication. The American population was also much smaller (scantly more than 1 million when Johnson's dictionary was published, and still less than 10 million at the time of Webster's publication), and public education was just coming into its own in the early 19th century. While 73 years is a long time, consider how long it is when there's no tradition of mandatory education to instill those spellings in youth: to this day, schools are probably the largest collective purchaser of dictionaries. Literacy rates weren't even first reported in the United States until 1870, so I daresay before the dawn of public schooling, there wasn't a lot in the area to brag about.
Webster's dictionary was first published only two years after the first public high school was established in Boston, and its growth in popularity coincided with the rise of public education. By the 1840 census, 55% of five- to fifteen-year-olds were attending primary schools: and you can bet your bottom that of those that could afford a dictionary (which I honestly couldn't estimate), they were far more likely to purchase a book published by an American than a Brit, if only because of availability and not for patriotic reasons.