It's not at all clear that America was supposed to be about this, even if that is what they teach in schools today. However since it's not really relevant I won't argue the point further.
> Do you have a counterexample? What non-democratic form of government do you consider free?
Many monarchies and similar governments throughout history have allowed more freedom for their citizens than today's democracies. Of course, no one is completely free under any of these governments (certainly not a democratic one).
> I guess, in a larger sense, I take it as given that a democratic and free society is a basic requirement for human progress...that make it possible for most to start anything new.
You really, really shouldn't take that as a given, especially that "democratic" part. It is understandable, though, that many people believe this -- considering it's essentially what has been taught in schools for the last century or so. Do you really believe enterprise did not flourish in the West until after the rise of democracy? That is not what history shows.
> what's to stop the political elite from taxing you at 99% of your income as soon as they think your widget would be fun to have? Nothing.
Not that I want your hypothetical to come true, but it is worth considering that tax rates in monarchies were generally quite low (<10%), especially when compared to the tax rates in today's democracies. There are well-understood reasons for this if you are interested.