For starters, humans don't NEED birth control or healthcare. Throughout history, prehistory, and even in modern times, humans just reproduce as many offspring as possible. Nature doesn't care about one's own personal happiness level. Nature will just select for the individuals with the highest reproductive fitness. Whoever is able to breed the most number of healthy, viable, fertile offspring will have their genes carried on for generations. This fact works very well throughout history and is complemented by morality (that it is wrong to abort or prevent a pregnancy).
However, in modern times, humans face a new problem. Humans have become so successful at breeding and eliminating causes of death that infant mortality and maternity mortality at childbirth decline, and that the life expectancy increases. With more people breeding and less people exiting the world, the world will become exponentially more populous, and soon, humanity will eventually run out of resources and space to live in.
Now, you may think, "Humans should stop engaging in sexual intercourse. No sex means no babies." While that is the most apt, rational response to this overpopulation crisis, that is not practical. And it is not practical, because too many humans are not rational. When you have irrational, stupid humans, someone will always do something stupid. Sometimes, this stupidity leads other humans to make protective guidelines for other humans. Other times, this stupidity makes babies. Combined with a nurturing and safe environment, these stupid babies grow up to become stupid adults, and the cycle repeats itself. Nature doesn't for rational intelligence. It just selects for who will breed the most offspring. If stupid people breed the most, then the future will be full of stupid people.
So, what does this mean for people who are both rich and smart? It means that they should control these stupid people. To control the population of these people, these stupid people should be given birth control. Humans already give birth control to deer and other mammals. So, giving birth control to humans is a non-violent way to prevent human overpopulation. It is possible to just legalize homicide, war, torture, genocide, forced sterilization, and the like on 99% of the global human population, but doing that would be extremely difficult, as most people in the 99% do not want to be selected out of the gene pool. They all want to be in the 1% of breeding individuals. So, what do humans do? The smart ones use their superior intellect to make birth control for the dumb ones. Making birth control costs money, so the rich ones should work with the smart ones to provide funding, legislation, and social pressures to prevent the dumb ones from making babies.
Because the purpose of birth control is contrary to one's evolutionary biology, some humans, persuaded by traditional moral beliefs, may be offended that they and their fellow humans are given birth control. Also, the human psychology must be taken into account. If the humans are made to feel inferior (that they are too stupid/irrational and thus make stupid decisions like having sex without the financial resources to take care of a child), then they will experience reactance and do the opposite of what they should do. They may even make babies just to spite everyone else. That's why creating the right language is important to offer birth control to stupid people who fuck too much.
If humans want to decrease the population, then the number of deaths must be greater than the number of births.
If rich, smart, and powerful people still refuse to finance birth control (including contraception and abortion services) for the poor, then they should not blame the poor for failing to rear the child properly. Poor people do not have the resources to give every child the same lifestyle and standard of living as rich people. Therefore, poor people should be free to let the child die. Let Nature take away the child's life. Infant mortality among the poor will increase, but that is to be expected and should be treated as a positive thing to thin out the number of people entering the world. Clean water access should not be delivered to the poor either, because clean water raises personal hygiene and public sanitation, thereby decreasing infant mortality rate among the poor. If humans want to decrease the population, then the number of deaths must be greater than the number of births.
Therefore, the poor, which constitutes the majority of the human population, should have two options. One, they should let their offspring (at least just the weaker ones) die and deserve no blame for letting them die. Two, they should be given birth control and be made to think that they have some control over their lives, even though it's actually the rich and powerful people who control the lives of the poor people by providing and enforcing the use of birth control.
My personal opinion is that national governments should all favor the latter option over the first option. The first option, while achieves the same goal, causes too much suffering in the world. Nobody wants to see their children die. Even if their children are weak, defected, stupid, or sick, parents generally don't want to see their children die. Parents always think that their weak/defected/stupid/sick children are going to live and thrive despite being the runt of the litter. There should not be a debate about whether or not people should be offered free access to condoms. Offering birth control for the poor (such as free biodegradeable condoms) is the only way for rich people to control the sex lives of poor and stupid people.