Being a good hearted boy scout is not the same as being a fascist. Miller's the one who made that link between the two (i.e. Superman is naïve and idealistic, and the government took advantage of that).
Given how Miller's take on Batman became THE portrayal of him that most writers have followed since it doesn't matter whether the average joe has heard of DKR. After 30 years or so of setting the tone for what Batman "should be" like, Miller's interpretation has pretty much become the definitive one -- Batman was certainly different prior to DKR -- and whether non-fans or even passing fans realize this fact or not is moot.
The same holds for Superman. DKR was the work that made them antagonistic toward one another -- broke their friendship and made them rivals -- and that formula has persisted ever since. It's also the work that, as I mentioned, made the link between Superman's boy scout attitude and being a stooge for the government. Whether the average person or fan realizes this explicitly is less significant than the fact that what Miller did was repeated by other writers so that, 30 years later, it's taken to be "canon" by many -- but not all -- readers.
The fact that the OP doesn't know where this take on Superman came from -- and the idea of Superman being a fascist was NEVER found prior to DKR -- says a lot (no offense to him/her). Miller ruined both characters in many ways, imo.