[WS:] But this was a while ago, no? Besides, guys like Thoreau were not settlers.
My take on it is a bit different, more institutional. In Europe, the state (monarchy) precedes the capitalist class and as such was the "default" embodiment of what we today call "public interest" (its the l'état, c'est moi thing.) The bourgeoisie (big and small) only gradually chipped away this state hegemony on "public interest" but a lot of that hegemony remained vested in modern state by default, so to speak (cf. the French republicanism.)
In America, by contrast, the capitalist class - plantation owners and industrialists precede the state. Not only did they found the US state, but they crafted it in such a way that it was ideologically and politically subordinate to the capitalist class, which by default held the hegemony for "public interest" (if this term is appropriate here.)
The state chipped away some of that hegemony away (especially during the Civil War), but by default a lot that hegemony remained vested in "private initiative."
In short, the American infatuation with libertarianism and private initiative is rooted not in some purported "settler mentality" (if there was ever such a thing) but in the blueprint of US political-economic institutions crafted by plantation owners and bourgeoisie that prioritize "private initiative" (i.e. the interests of plantation owners and industrialists while paying lip service to smallholders) before the state. This institutional blueprint changed remarkably little in the US (vis a vis sweeping institutional changes taking place in Europe and Asia in the same time) - which may explain the popularity of ideological expressions of that institutional blueprint.
Wojtek