>The best way to "control" population growth is...
Then provide some level of govt incentive to reach that goal, it's still coercion (or if you prefer, manipulation), even if the incentive is 1st order positive effects, and the stated goal/result is a 2nd or 3rd order effect.
Thinking about it, I keep coming back to preditory lending/selling tactics or dark-pattern manipulation (except the UI is your life choices) as comparisons, but I haven't worked out exactly why, yet, other than it bothers me in a similar way. Moreso, since it's government.
It's a coordination problem. Everyone wants to act in the way that maximizes their happiness/success/utility, but in doing so acts in a net-negative way. One of the premier purposes of government is to solve coordination problems. Why is it unethical for the government to solve this coordination problem?
Or, more concretely, why does my right to have a dozen children trump my children's right to have sufficient resources left to them to live a happy life?
People are free to use or not birth controls if they want or not children, same for the education. People aren't tricked in reducing the amount of children they have. Data in developed countries seems to point that when people are better educated and have the tools to decide for children, they get them later in life and in less quantity (without considering other factors, such as religious communities that have more children per woman than average).
How would your opinion change if that correlation were found to disappear in the coming decades? Or if it actually began to reverse (for example as populations shift to being more urban where kids are expensive and access to assisted reproduction depends on wealth)?