There is a whole slew of problems.
1) There is still an expectation women will marry up, and men will marry down, in terms of income potential. If the woman is a little bit ahead, it's okay, but e.g. a doctor marrying a nurse is perceived as acceptable in one direction, but taboo in the other. This means there is a growing shortage of mates for men at the bottom of the socioeconomic heap, and increasingly, women at the top (unless college-age and pretty).
2) Overlapping and poorly-defined roles make for a lot more conflict in marriages.
3) Divorce laws vary by states, but in the most liberal states, tend to be punitive towards men; the de facto standard is women get the kids, and men pay (massive, debilitating) child support. At the same time, the legal industry works hard to increase divorce rates. With half of marriages ending in divorce, this leads to all sorts of misaligned incentives and imbalances which are taboo to talk about, but interplay in complex ways. Marrying down is now a huge liability.
4) And, as you pointed out, social classes are much more likely to calcify.
We kind of got to where we are randomly, without thought or planning. We had a bad system (women were oppressed), and we pushed hard against it. It snapped. We landed somewhere pretty random and still pretty dysfunctional; just dysfunctional in other ways.