This may be true historically, but does it have to be that way going forward? My thoughts, not based on studies but based on people I know, is that the general interest in marriage has declined as there is a preference for greater autonomy amongst both men and women, not to mention economic independence. Marriage was born out of economic need, and was given a religious stamp of approval. If the same economic need isn't there, and developed countries are becoming more secular in their beliefs, it would seem only natural that marriage rates would decline.
But that doesn't mean people don't want children, or can't have children. With the introduction of ivf, and both egg and sperm donors -known or unknown- its possible for the birth rate to be maintained. It may sound bizarre now just as putting ones profile up online in search of a mate was at one time, but it could be become the new norm. Search for gametes the same way you searched for a partner at one time.
As far as the maladies of single parenthood go, much of that may be attributed to the education levels of the single parent and/or their poor economic circumstances. It doesn't have to be that way though. Of our last 4 US Presidents, 2 pretty much grew up without having a reliable father around for most of their life. They seemed to both have had pretty smart moms.