Reading well regarded works such as The Roman Family (1992)
https://books.google.com.au/books/about/The_Roman_Family.htm...
strongly supports that in Roman times, just as today, there was no single concept of family. While the “nuclear family” was central, divorce was common, as was remarriage, resulting in blended families. If a parent died, a child was sometimes fostered by extended family.
It appears that one of the greatest differences between classic Roman times and modern US customs might be the extent of extended family support, that difference perhaps also seperating modern US customs from many other modern countries.
And does it retell of the common Roman, or of the Roman elite? These tales may be radically different, from what I understand.
I expect the Christianized Romans would have had more laborious conventions such as we see with the Catholic Church in the middle ages. But I'm extrapolating.
Your "latter Christianized Roman Empire" was the dag end of a rotting corpse .. you might be thinking of the Byzantine Empire (aka Eastern Roman Empire)
Republican Rome and to a much much greater degree Empire Rome were not entirely homogenous, the Empire integrating many cultures (such as the Arabian divisions building Roman forts in Britain) .. much as modern USofA does with it's large latin and many other demographic populations.
The Roman Family picture would need to be broken down almost as much as the US Family picture - I suspect the single parent rates in the US might vary considerably by ethnicity .. although it's interesting the the article linked above (IIRC) suggests that Christian V. non Christian rates are more or less the same.
My presumption is that the later Roman empire, despite its collapse, did inform the later customs of Europe, particularly in religion if only due to incidental diffusion. And by that dint also affected the custom of marriage, divorce and perhaps more importantly the status and autonomy of women, though I've all but forgotten precisely how this all played out. And I may very well be mistaken.
I would also posit that it has less to do with religion and more to do with [perceived] female autonomy, value, mobility, economics, and the abatement of the stigma of divorce. The religious aspect having only been the foundational institution of the customs which have been carried (somewhat steadily) forward for nearly 1500 years let's say - a tradition which has suffered a colossal usurpation in society's working memory.
I think it's important to note that women with children are not necessarily unbounded as are women without, I think it would be difficult quantify pre- and post-divorce expectation shifts, but I believe it would be an incisive question. But if the expectations aren't grounded in reality the decision weighing process would lead to poorer outcomes.
Why later?
Roman Law was the foundation of modern Western Law and it dates back to Republican Rome with a lot of fleshing out during peak classic Empire Rome.
Both Greek (pre Rome) and Roman attitudes toward women have persisted to this day; in Greek stories Telemachus tells Penelope to shut up, and Philomena has her tongue ripped out by Tereus so she cannot speak of her rape .. these are the templates for the active, loaded silencing of women today in public life.
On that theme you might enjoy Mary Beard's Women in Power lecture (part of a series).
[ Dame Winifred Mary Beard, DBE, FSA, FBA, FRSL, English scholar of Ancient Rome ] https://en.wikipedia.org/wiki/Mary_Beard_(classicist)
[ text ] https://archive.md/mAoSZ
And what I mean by this is that we've, for example, still got houses built for whole families, yet the families have so often been split. The density doesn't work and there isn't enough of the intermediary to go around, and it seems like that has been a multi-decadal problem at this point, which has been growing enormously. Houses are neither fit for a return to the nest, and they aren't suited for bifurcation so neither can we expect people to live in multigenerational households nor can we expect the constituents of a family to remain in close proximity (nor should we, in many cases). That then further complicates things, once trivial obstacles require resorting whole days, perhaps weeks. And if a coparent is unreliable - by God will that drastically complicate one's life, sometimes it's easier just to cut away, whole cloth.
Whether that was a good and noble thing I can't dispute. But it was done with little foresight, and I can hardly say if my own perspective - that lack of foresight, of prescience, is just characteristic of my own privileged hindsight - but I think it's evident we're in a poorer place because of it. But it's sort of besides the point anyways as we're here and now.
And it may appear easy to just say "Well, I'll stick with ye olde convention." But I don't think it's the case as everyone, myself included, wants their cake and to eat it too. Fantasy and reality are more miscible than ever before. Apparently normal people with reams and reams of their life's perfectly orchestrated highlights on shining beaches sunken in beautiful blue oceans with perfect partners - except they're buried in debt and have median income and fight incessantly, but they copy type well enough and edit even better so nobody knows they've got skeletons in the closet. And these are the kind of standards we're all sort of inadvertently supporting. And with that unreality we convey ourselves into deeper depths. But that's old hat, everyone knows it (or everyone I know does) and yet we're still marching off in that direction because — still — nobody knows what the fuck we're doing, and it won't be plain to see until some very hard times come, I reckon.