Hmmm… nobody’s mentioned the obvious - it costs a fortune to get married properly. The amount some families spend on the (daughter’s) wedding is ludicrous, sometimes more than the family can afford. SO the poorer women, the ones who left home and have no parents to help pay for things, possibly consider putting off the wedding until they can afford their “special day”. Unless, of course, they latch onto a guy who can afford something close to their dream wedding, or at least something better than a trip to city hall in clean clothes. (Which still seems to some as the losers’ way.)
Rich people, too, are more likely to formalize the relationship to handle the legal/financial loose ends. There’s a lot of situations where living together qualifies as pretty much the same as married, but a lot (IIRC) where it may not. Home ownership and names on title, and the disposal of assets in break-up, custody - all these matter to people who can afford houses and afford lawyers for protracted arguments over custody of children, but less to those who cannot afford such things, nor the stability to contemplate needing them. In fact, not tying the knot makes breakups for the poor simpler and more flexible - and much cheaper.
Not sure the Appalachian example applies, I recall from many years ago (have times changed?) a woman could be kicked off welfare if there was a hint she was entertaining a man regularly in her place. This is the common inner city complaint that the welfare system actively encouraged the single mother problem, since a guy who spent too much time at his girlfriend’s house could be deemed her new means of support.
(Plus there’s the jail problem - in inner cities, stats says something like 1 in 4 men of not-in-college marriageable age (say, 18-24) would have spent time in jail, or 1 in 10 ARE in jail. This not only means there are fewer men to choose from, and they are less likely to find permanent employ - but the differential leads men to exploit their status. IIRC from a NY Times discussion of the issue, one woman who confronted her boyfriend about him seeing other women got the reply “I didn’t realize you expected this to be an exclusive relationship”. As men in China (and India) are finding out, it does not take a large differential to make the scarcity an issue.)
Finally, with money and careers comes planning. People who have decent incomes probably give far more thought to the timing of having children… sometimes too much though, and think themselves out of having children. For lower income groups, likely along with less education comes less planning and less carefulness. Fathers who are surprised by unplanned pregnancy are probably more likely to leave, especially if they have no assets or wages to be chased for.