There are differents versions of the story. The one you are mentioning is emphasized by Christian theology mainly. At the end of the day these are all myths, and you are right, in this version it is emphasized that Adam and Eve represent the original "sin" of humanity. The Christian Church has always used this guilt to control people as much as possible. In Judaism this concept of guilt is basically non-existent, they place zero focus on it, it's just a weapon that they use on Gentiles.
In Yehuborim Midrashic literature (there are mentions in some kabbalistic texts as well), it is stated how "Samael" (Satan) and other Demons refused to bow down to Adam (Yehuborim). The same thing is also mentioned in Yehuborim Islam, where this same theme is very significant.