Because the people popularising "exceptionalism" are idiots
And don't quite understand what it is that makes the American system unique or functional or even superior.
It isn't that phrase, because governments around the world have now adopted some semblance of a republican virtue of self-ownership and self-determination. The variety of such is of course extreme, but as noted, a very secular country like say, Denmark, or even (supposedly socialist) Sweden possess actually considerable freedoms endowed to their citizens which their governments are bound to protect. The Danes in fact seem to come out "freer" routinely even on quasi-empirical "economic freedom" models used by right-wing American think tanks. There are gradients where these countries also use generous welfare states that American voters recoil and flinch from, largely because of their redistributive tax policies and emphasis on raw cash transfers instead of the inefficient transfer payments that we tend toward. But it is also much easier to start a business, run it out of your home, and so on, practical and meaningful freedoms that many Americans lack (not to mention fewer counter-productive moralising restrictions on narcotics, prostitution. Or fewer restrictive air travel screenings).
Freedom is not merely a straight line beyond which only Americans, much less god-fearing Americans, possess a such thing, and the sooner we understand this the easier it will be to improve our situation where we decide what to do with those tyrannical behaviors and government restrictions in our own society rather than to pretend that no other society may have a learned or practised freedom that we lack whilst protesting loudly and with impassioned speeches about a rhetorical freedom that we do possess instead.