The result is that over the next 50 years, while peace and prosperity reigns due to the guiding hand of the Overlords, marriage, traditional morality and organized religion all vanish.
Of course, Clarke actually thought this was a good thing, and the rest of the novel is about humanity moving onto the next stage of evolutionary development: as a non-material group mind. But in a sense, that's the really interesting thing, that as someone who saw traditional marriage, morality and religion as a problem back in 1953, Clarke say the two inventions most likely to get rid of all three as being completely reliable contraception and paternity testing.
Coming at things from a Catholic point of view, G.E.M. Anscombe saw the same trends, now well advanced, in relation to contraception, morality and marriage in her 1972 essay "Contraception and Chastity". Some key bits:
I will first ask you to contemplate a familiar point: the fantastic change that has come about in people's situation in respect of having children because of the invention of efficient contraceptives. You see, what can't be otherwise we accept; and so we accept death and its unhappiness. But possibility destroys mere acceptance. And so it is with the possibility of having intercourse and preventing conception. This power is now placed in a woman's hands; she needn't have children when she doesn't want to and she can still have her man! This can make the former state of things look intolerable, so that one wonders why they were so pleased about weddings in former times and why the wedding day was supposed to be such a fine day for the bride.
There always used to be a colossal strain in ancient times; between heathen morality and Christian morality, and one of the things pagan converts had to be told about the way they were entering on was that they must abstain from fornication....
Christianity was at odds with the heathen world, not only about fornication, infanticide and idolatry; but also about marriage.... But the quarrel is far greater between Christianity and the present-day heathen, post Christian, morality that has sprung up as a result of contraception. In one word: Christianity taught that men ought to be as chaste as pagans thought honest women ought to be; the contraceptive morality teaches that women need to be as little chaste as pagans thought men need be.
And if there is nothing intrinsically wrong with contraceptive intercourse, and if it could become general practice everywhere when there is intercourse but ought to be no begetting, then it's very difficult to see the objection to this morality, for the ground of objection to fornication and adultery was that sexual intercourse is only right in the sort of set-up that typically provides children with a father and mother to care for them. If you can turn intercourse into something other than the reproductive type of act (I don't mean of course that every act is reproductive any more than every acorn leads to an oak-tree but it's the reproductive type of act) then why, if you can change it, should it be restricted to the married?
Today, we can see pretty clearly that both Clarke and Anscombe were right.