Wikipedia article on him repeatedly says vague amounts like “several 13-15 year old boys” but does that mean like 4 or 4000?
Also what was going on at the time that a guy that was likely himself a pedophile (?), was in charge of giving neglected orphans to convicted pedophiles? Why didn’t that plan get nipped in the bud the second he said it out loud?
As disappointing as it is, the number of children involved is still unknown. This is due to several factors, the largest of which is just that they covered their tracks pretty well. Although it was known or suspected in certain circles, it didn't really come to light until 2015 (source). Even after that, it wasn't widely known, and it took until 2021 for the German government to sponsor an investigation into it (source). They stated
The Kentler case is not yet closed. Due to suspicions about a network and nationwide scope, further reappraisal and research are necessary. That is why I have commissioned a third research project at the University of Hildesheim with the task of investigating possible nationwide links
--Sandra Scheeres (SPD)
A large part of the reason why it's so hard to find exact numbers and records is because Kentler & co. were very careful in covering their tracks. While we know that it happened, and we know their general goals, the exact adoption and foster records are hidden or missing. Despite their own beliefs, they were very aware of the prevalent social views on their experiment, and as such, kept it mostly buried. There's a reason he didn't publicly mention it until the statute of limitations had passed.
There's also just issues of anonymity. Even as more of it is brought to light, they want to keep the identities of victims secret in order to give them all possible privacy.
As to why Kentler was allowed to get away with it, that answer is a little more tricky.
For one, he was extremely famous and well regarded.
Kentler was a well-known scholar, the author of several books on sex education and parenting, and he was often quoted in Germany’s leading newspapers and on its TV programs. The newspaper Die Zeit had described him as the “nation’s chief authority on questions of sexual education.”
So, he was a trusted figure who supposedly knew a lot about this topic. Although looking back with our modern perspective, we can clearly see how categorically evil this was, it's easy to forget that we have the benefit of several decades of cultural progress and knowledge. Pedophilia wasn't fully understood yet, and was far more acceptable.
In 1959, around when this experiment started, Hawaii's age of consent was 14. Georgia's age of consent was 14 until 1995 (when it was increased to 16). Hell, even in the 2000s, there were cases of loopholes in laws that would cause underage girls to be forced into marrying their rapist, or being denied the opportunity to divorce an abusive older husband (source). Gabriel Matzneff wrote openly about his pedophilia, and was friends with a number of important French government officials, journalists, and businessmen. He wasn't arrested until 2020 (source).
There's also the fact that West Germany was desperate. As their government was forming, WWII had left over a million children orphaned and homeless (source). This problem persisted into the 1960s. They barely had the capability to manage basic government tasks, they didn't have the capacity to build a comprehensive care network for the children. This is also part of the reason why finding records is hard: Kentler took advantage of the chaotic state, where records were often poorly kept or nonexistent.
The sad fact is, he was powerful and famous, with a number of important friends in the government. Same story that repeats across history: people with money and power tend to do a lot of horrifying shit. People in the government went along with him because they were close to him, or because they genuinely believed this "expert" was right, or just because they wanted a problem solved and didn't particularly care how it happened, so long as their hands were "clean". There are instances of people looking into it and trying to help the children... which were crushed by Kentler and his reputation.
Edit:
Going a little more in depth of Kentler's actual motivation, because I realized I never addressed it. I should stress that the second half of this is psychological analysis, which can be dangerous in history. However, in this case, he died relatively recently (in 2008), we have a number of his writings available, and he spent a great deal of time around other psychologists who have since been able to profile him. He also fits the stereotypical psychological profile almost perfectly Because of this, we can draw some conclusions, very cautiously.
In response to the semi-question in your post: Yes, Kentler privately admitted to a friend that he'd sexually molested his own son, and there have been a number of other credible allegations of child abuse. He believed that sex between parents and children was normal, and that it should be encouraged, as should sex between adults and children, so long as it was mutually pleasurable. Similar to how many parents encourage their children to try drinking for the first time in the home, so that they can get used to it, Kentler argued that this would actually prevent abuse by teaching children what a pleasurable and consensual relationship looked like.
THIS IS OBVIOUSLY COMPLETELY WRONG AND HORRIFICALLY IMMORAL.
The most simple analysis is that Kentler had a desire to sexually molest children. He desperately needed that to be normal, to be right, because otherwise, he'd have to accept that there was something fundamentally wrong with him. It also fits with the actions of someone who has been abused by a parent: he couldn't make the image of a loving father and child molestor fit, so he decided that it must be normal in order to avoid confronting that what had happened to him was wrong.
Also, upon looking into it more, it wasn't quite as well hidden as I thought. 2015 was when the broad public became aware, but he'd mentioned it in his book in 1989. A feminist newspaper called Emma had reported on it, leading him to be shouted down by a group of women when receiving an award, and punched in the face at a later time. It also cost him an award. However, as mentioned previously, it didn't really reach the public awareness until later. Part of that was likely due to the fact that his book wasn't really read outside of academic circles, many of whom were predisposed to agree with him. Those who challenged him were shown his "evidence" that the program had worked (spoiler alert: the evidence has been routinely and thoroughly debunked).
A large part of why it took so long for the government to act was that there are a large number of people still in power who were involved (or who are connected to someone involved, or owe their career to one, you get the idea). On top of that, no politician ever wants to admit "Yeah, our government deliberately allowed pedophilia".
Sort of tangential, but the comments here, and follow ups here by u/gerardmenfin about the respectable side of the paedophile movement in France, and its decline would probably go some way to contextualising your last question. At least it helped me understand the general attitudes at that time a lot better.
(also you're shadowbanned)