Should people require a mandatory license for parenting?

why is everyone allowed to rule over helpless human beings

The answer is more or less contained within the question.

Even before we get to deeper matters, I've got to question your enforcement methods. How would you prevent childbirth in unqualified couples? There really aren't easy, inexpensive, reliable, side-effect-free and reversible methods of preventing pregnancy (IUDs and implants are the most effective, but aren't tolerated by a non-trivial portion of the populace). Nor do these seem likely to be developed in the near future. Even if they are developed, there are pretty strong social norms involving bodily integrity, especially related to reproduction -- and honestly, I'd hope these norms continue to become stronger. Likewise, there are other norms that seem unlikely to weaken dramatically if we were to discuss, say, forced permanent sterilization, forced abortion, or ripping infants from the grips of tearful mothers.

How would you limit 'assignment of children to religion'? Does it become illegal for bring a child to church? To pray at home? Even if social norms regarding freedom of religion disappeared overnight, the difficulty of enforcing such a system is rather severe.

AFR and adoption have strict criteria not a solely as licensing mechanisms, but also because there are high costs and limited supply -- a natural limitation. That's not really the case going the other way around.

At a deeper level, there are some non-intuitive economic reasons that essentially guarantee any entrenched democratically created licensing system undergoes regulatory capture, and serves the interests of licensees rather than those individuals it was made to protect. This system does not have a method for opposing such capture.

Children should not be assigned with any religion.

and

Parents should be forced to allow their children to take part in a educational framework based on contemporary ethics and knowledge.

So by your standard it is okay to force children to take part in state mandated indoctrination, but not in parent mandated indoctrination. Why not take an even hand and allow children to direct their own learning?

Bad parents wouldn't be so much of a problem if children were considered communal, rather than individual, responsibilities.

While I instinctively approve of licenses to parent, when I think on it I wonder if that might be too counter to human nature to ever enforce successfully.

And my deeper feeling is that it's the "two parents have a kid, so the kid belongs to them" culture that causes a lot of the problems.

Turns out that some parents do require a mandatory license for parenting. A parent can end up before judge and be required to take a parenting course. These courses are all (as far as I can tell) evidence-based, developed and evaluated using sound science. Programs like: Incredible Years, Triple P, Kazdin Method.

Ironically, most parents, even those who read lots of parenting books, never encounter a parenting book that is primarily evidence-based. Most parenting books are opinion-based. The most recent evidence-based book that I know of is "Everyday Parenting" by Kazdin.

This sounds like to me as though it's essentially a giant recapitulation of the trolley problem - you have one side claiming that the opposition doesn't understand 5 > 1 and isn't trying to maximize utility and should be pushing the fat man onto the tracks, and you have the other side not wanting to violate obvious moral norms such as "Don't push people onto train tracks where they will die" for the sake of hypotheticals that are not merely unlikely but unrealistic. (How is that man so fat that he'll block a trolley going fast enough to crush five other people, anyway?)

Then the first group argues that sometimes you need to be able to engage rational overrides when the situation is different from what you're used to (or adapted to) and in this case we're stipulating that the man is fat enough to stop the trolley if you push him onto the tracks, and the second group argues that you want bright-line ethical rules and guards against corrupted hardware and con artists trying to convince you to do evil deeds "for the greater good".

In this case a bit less freedom would guarantee a lot less distress.

If this statement is to be taken as a hypothetical stipulation similar to that of the trolley problem, I agree with the hypothetical breeding license.

As a real-life policy suggestion, though, it sounds like a terrible idea due to violating a lot of people's moral norms (which will cause distress), having implementation difficulties (who will make/mark the tests for getting a license), being prone to frighteningly nasty abuse, and underspecification. Please do not take my support of the hypothetical stipulation as being in any way supportive of the actual policy suggestion.

The Family-Teaching Association certifies group homes in the use of evidence-based parenting methods. Everyone involved has to be trained and meet standards. These group homes have replaced what use to be call orphanages. A resident family-teaching couple has the role of parent for a group of kids. The organizations managing the group homes also provide support for troubled families as part of an overall system to deal with severe problems related to bad parenting.

So, at least, there is a licensing system geared to addressing the consequences of bad parenting.

Boy's Town is part of this system. It was an early adopter of evidence-based parenting that converted to family-like group homes in the 1970s. Perhaps a rare occasion when a religious organization was on the cutting edge of science.

You raise interesting questions. However, I don't think you give realistic solutions. Someone's decision to let someone have a license would be biased, wouldn't it?