My guess is, for the Scion's at least, is they didn't awaken to the Echo because it wasn't really them. As for Ryne, I don't know about her. I don't think she has the Echo, at least the way Minfilia did, but she does have something, being the Oracle of Light and all.

Eden spoiler
In E8 Ryne becomes the vessel for Shiva, similar to Ysayle. However, unlike Ysayle she loses control of herself. Originally, possession of the Echo was thought to be the reason for Ysayle's maintained control. However, it was proven that the summoning of a Primal into one's self does not mean they lose control, as both Thordan and Yotsuyu still retained their sense of being. But Ryne is not as experienced in life as the other three individuals, so that is probably the main reason.