I think that the possibility that parents coming from a better economic status might have the free time and resources to attend to their children more, leading to secure attachment, and be able to provide better for their children, allowing them a better education and quality of life later on. It is possible that this external factor can explain the trend of secure attachment correlating to a better quality of life later on.
I agree that socioeconomic status can play a part in attachment. If a child comes from a family that can provide more resources, the child is probably much more likely to form a secure attachment. It's possible that lower income families work longer or more inconsistent hours in order to provide for the child, so the child is unable to see his or her parents as frequently as a child coming from a higher income family. However, I don't necessarily think this is the only influencing factor for creating a secure attachment.
I think that it's probably true that the economic background of a family could impact the development of attachment. The lack regularity in the lives of lower income parents and the fact that they are likely to . In addition to having more time and a stabler environment, higher income parents are more likely to have the eduction to know about parenting techniques that facilitate attachment.