A picture valid for most modern jurisdictions, common and civil law alike.
First, it is good to understand that the child support is owed to the child and not to their mother.
It may be the mother who manages the child support, but it is clear that the mother manages the funds as an implied trustee of a child and not as a beneficiary.
There are cases when both genetic parents are forced to pay child support for a child born by a surrogate mother and even more cases when the mother is forced to pay child support to a child who lives with the father.
The whole idea of the child support stems from the fact that the child is not an object owned by its parents, but a separate human being and even a citizen with its own rights, including, but not limited to, the right to get an adequate and responsible parental care until their adulthood.
The moment when the child becomes a human being with its own rights varies by jurisdiction and is either the moment of birth, the moment of conception or some other point in between.
The responsible parenting is owed by both parents and the obligation cannot be contractually altered or transferred to other parties because it does not emerge from a contract in the first place. The existence of a child alone implies the obligation.
This is much like the taxes - you owe them, period.
The rights of the child are legally protected to a higher extent and with a higher priority than almost whatever other rights the parents may have. This is because the child is considered a vulnerable member of the society.
The question of the intent (or lack thereof) of conceiving a child is so much minor in this context that it is almost never considered in the court proceedings.
This is a profound contrast to the penal proceedings where the intent is a central point. Being a parent is not a crime in itself, so the intent is not important. You are either a parent, or not - and the possible intent is only good as long as it helps determining your status as a parent.
The parenting obligation can be transferred by other means, e.g. by adoption, but the whole adoption concept is also shaped around the interests and the rights of the child.
In regard to the "consensual sex":
The traditional view of this thing is that both men and women engage in sexual intercourse with the clear knowledge that a conception is a possible outcome. Yes, it implies a great level of trust between the partners.
As much traditional is the understanding that a woman cannot escape the parental obligations, but a man can - because he can plausibly deny the fathership.
This possibility has never been a "men's right" in the first place, it was just that - a possibility to avoid fulfilling a legal and moral obligation.
It is no more that much easy because of the technological and the social advance and not because something happened to the "men's rights".
It is also not much of a discrimination - the obligation is for both parents and this was never really disputed.