I mean I wouldn't say that's the image they project. their tv shows and films are shockingly prudish. push any violence you like, but heaven forbid you show a tit
they also have this thing where everything has to have a moral. even things that are seemingly immoral - it's always sunny, south park, etc - do in fact have a moral message. the message being "if you're doing the things our characters are doing, you're immoral"
Using sociopathic/immoral characters in situations where they should reflect, but dont (or take the "wrong" stance) is a trope that goes back to Seinfeld. They are not deliberately/exclusively trying to make a value judgement. Usually it's social/political commentary specifically designed to shed light on how awful Americans can be to each other. It's (subjectively) funny because we have encountered milder forms of such people in real life, perhaps.
I agree that we are prude as a culture, just dont see how this is evidenced by the average sitcom. South Park in particular is a very strange example of a "prude" show.
they also have this thing where everything has to have a moral. even things that are seemingly immoral - it's always sunny, south park, etc - do in fact have a moral message. the message being "if you're doing the things our characters are doing, you're immoral"