Given that humanity has evolved from what we believe were such species, I would expect that any such society would not be as successful as ours. We evolved our current forms of sexuality precisely because they were more successful.
In your description of human sexuality you miss the most important factor behind the vast majority of human sexual activity - it is an important part of human pair bonding. Recent studies suggest that when it comes to conception women are actually programmed to seek very different partners to those they would form a relationship with. Even at a base, instinctual level almost the entirety of the sexual activity within this relationship is motivated by the desire to bond and form a closely knit unit, and not to conceive. Without this "recreational" sexual activity, it is unclear to what level male/female relationships would develop. Without the support of such a relationship, new and expectant mothers may face significant difficulty.
In humans, as compared with other species, the male and female are remarkably equivalent in the overwhelming majority of qualities and abilities. However, relative to other species, human pregnancy is especially restrictive - a heavily pregnant cow is not nearly as restricted in its movement as a heavily pregnant woman. Worse, excessive exercise during pregnancy is heavily associated with miscarriage - and strenuous agricultural work would be more so. This means that for a period of time a pregnant woman will contribute less and demand more. Also, human newborn are unusually helpless for an unusually long period of time - it is perhaps 4-5 years before they have any real hope of fending for themselves, and much, much longer before they have a good chance.
Now, it is possible that a woman will be sufficiently supported by her family or wider society, but there are difficulties here. 1008
Firstly, in an early agrarian society life expectancy is short and mortality at all stages of life, especially infancy, is high. Even in our own world, the typical response to high infant mortality is a higher birth rate. Families will most likely be very broad but lack depth. Relative to modern families there will be fewer elderly relatives per young child, less attention to go around, and less spare capacity in the system to support them. The "dreadful algebra of necessity" creates a kind of terrible paradox for children - they are both loved and unwanted, both essential and disposable. In our own world, impoverished children have had a terribly bad lot in life and most societies throughout most of history have done very little to help. It seems unlikely then that a pregnant woman or new mother, unable to depend on the father, could reliably depend on significant support from society. Furthermore, by limiting the development of pair bonding, any "family" will be restricted to female ancestors and their descendants (of both sexes). Realistically, extended families will comprise somewhere between a quarter and a half of the individuals that would have been included in a pair bonded society.
In a bronze- to iron-age society, I would expect all of this to dramatically increase the depth and duration of periods of poverty and hardship, exacerbating food shortages and severely limiting the supply of surplus labour that could be turned to technological development.
As for modern society suddenly catching the disease, I have far fewer fears. With the high levels of social security enjoyed by modern civilisation, established charitable organisations and well developed systems of state support, society would largely continue unchanged. There would probably be increased pressure on housing as people lived separately rather than together, but otherwise we know that single parents and their children are able to live very good lives. 998