I only wish that were true. There are too many around here who want to establish a totalitarian police state cum theocracy instead, and it is this confusion and attempt to hijack the "conservative" agenda which used to be called liberal until New Deal Liberals hijacked the word and caused all sorts of confusion between a liberal, who is a conservative and a Liberal who is not liberal.
You are quite correct that American conservatism is more or less indistinguishable from classical liberalism.
European conversatism has always been a different animal, with various elements of blood and soil or church and king.
Consrvatism inherently describes an attitude resisting change. It does not describe, of itself, what change is being resisted or what is being conserved.
Thus Gorby’s “leftist” opponents were actually conservatives, as they were trying to conserve the Soviet system.
Can be very confusing.