One of the things that sets us apart from our close genetic relatives among the large primates is that human females do not have obvious visual queues as to when they are fertile. Sure, as every NFP using couple knows, with enough study we can figure these things out with a fair degree of accuracy. But it's certainly not something where you can simply look at your wife from across the room and see, "Ah, fertile at the moment, are we."
By comparison, when researchers are watching bands of chimps, the physical signs of a female chimp becoming fertile are so obvious that the researches can spot them from a distance. And the male chimps certainly are not in any doubt. (Of course, it helps in this regard that chimps don't wear clothes, but you get the idea.)
It strikes me that as humans became, well... human, and our social structures began to develop, that the fact that it's not readily obvious when women are and are not able to conceive probably helped to re-enforce the need for marriage (or stable mating arrangements, if you want to sound all analytical about it) and for family social structures. This lack of certainty created a need for social structures that emphasized long term fidelity.
Thinking about it this way: our lack of certainty as to whether any given act of intercourse will lead to children is one of the aspects of the human creature which had a fundamental influence on how societies developed. Or put it in moral terms: this physical reality reflects the intention that families be based on permanent fidelity.
All of which suggests that the advent of generally effective birth control would be very socially disruptive. (Which I think one could certainly argue it has.) And that if 100% effective artificial birth control were developed (which could be turned off and on at will yet allowed no user error or failure) it would be even more socially destructive.
In a strictly cultural sense: the social structures we're used to surrounding marriage and the family are based on the assumption of not knowing when sex will result in offspring. In a moral sense: that physical reality reflects that we are creatures who are made to work a certain way -- and our morals surrounding marriage are the "operating manual" for how to live successfully within that reality.
When we change these things, we in some real sense change who we are.