Interesting topic OP. I can see how and why you came up with your conclusions but this is just my humble opinion - I think it's not accurate and I'll explain why below.
I have an 11 year old son that plays hockey here in Edmonton. He started late (7-8 years old in Novice) which was 4 years ago. He learned to skate young (about 3) in those learn to skate programs but he was functional - not good. He joined hockey and was placed in the worst tier (6). Last year (though messed up due to Covid) he got into tier 1. That's still not elite for his age group as there is double-A (which you have to apply for and try-out) and someone also started something called a super league (which may also have much better players though I'm not very knowledgeable about it). But he's improved a lot.
We have gone on quite a journey to improve his hockey skills and I have learned a lot about what is needed to be a good hockey player. Hockey is much different than other sports as the skills needed are quite unique. You need to really develop your gross motor skills in order to excel. Hockey requires excellent skating (therefore need to practice it a lot), great stickhandling (again need to practice a lot), ability to shoot, hockey IQ, and strength and power (which means learning which exercises are needed to produce the effect you want) to skate well, stickhandle and shoot. And then you need to be able to combine all of the above skills together to be effective.
I put my son in a bunch of camps around Edmonton to improve all the above. Some instructors are very knowledgeable and some aren't. And even putting him into a bunch of camps doesn't mean anything. Instructors aren't able to provide personalized coaching to your kid. So it's either up to the kid to figure it out or the parents and child to figure it out together.
In any case, I strongly believe being knowledgeable about hockey (which former players are) gives their kids an advantage. And that is why their kids end up in the best league in the world more often.
Going back to my kid as an example, I put him into a bunch of edge and skating classes to improve his skating and stickhandling classes. It did help him improve but to get him to the next level I had to become knowledgeable enough about all these different aspects to get him to the next level.
For skating, when to use what technique in given situations, for stickhandling we had to learn dribbling because in order to look up while you are skating you need to dribble to puck and back and forth to know where it is without looking down. For shooting, how to shoot in stride, how to change angles of your shot etc. To be effective you really need to build a base and you need to build a lot of these at the right age or it becomes harder for kids to excel as they move up.
With kids of former players, the Parents understand all this and put their kids in the right camps, with the correct instruction and then they are able to provide their own expertise to help their kids excel.
Hockey is quickly becoming a sport with specialized knowledge. If you have it or can pay for someone to provide it to your kid, they will have an advantage. If you don't know this then your kid will likely struggle.
I didn't know any of this when I started out.....I have had to do a ton of research and learn a lot along the way. And I made so many mistakes. In the first year, I put him into hockey year-round (winter & spring hockey) with lots of camps cause I thought that was the way to improve (using Malcolm Gladwell's 10,000 hour rule as a guide). I then learned that was one of the worst mistakes parents can do (in any sport) after I read an ESPN article about the damage year round basketball was having on kids in the US (also researched a bunch of development models in Canada, US, Sweden and Finland to learn of my faulty logic). His first year going into Atom I made him jog with me for 20 min 3 times a week and learned afterward how that is one of the worst types of training for hockey players and will diminish how effective they are on the ice. Even something as simple the right stick length eluded me. I was shocked to see how the right stick length will improve skating for example.
This is all something former hockey players already know and can impart that wisdom on their kids and thus giving them an advantage in the development phase. That is why I think you are seeing more former NHLers kids in the league.
Also, I haven't read all the posts in this thread (just the last page). I see some discussion about genes.....they obviously matter but I encourage you to read the book "The Sports Gene". It will make you rethink your "genetics" angle.
Also, someone mentioned that the internet now has all the training information anybody needs to excel these days so it shouldn't matter where they are from. This statement is kind of true but I will say for hockey, the training information is not as readily available or organized. Lots of information out there but some of it is accurate and others exist for monetary purposes only. Just research "right stick length" and see what you get (hint: you will get lots of posts about your chin, nose, eyebrow, etc but none of it is correct). And the right stick length will impact proper skating to such a great degree as well as stickhandling but it's crazy that it's so hard to find).
This is very different for other sports. For example, for my son to learn and improve in basketball, baseball and lacrosse was much easier. There is much better information available for those sports vs hockey.
That is why having a former NHLer is such an advantage for these kids. The development model is more laser-focused and proper/accurate. The kids get the right information, at the right time to accelerate their development. And as others have said, I think if you don't have money, hockey is a very difficult sport to play and/or excel in. I have learned a lot but I don't think I could have without spending money on camps to see what they were doing and trying to understand the logic and then learning. So I could have researched on the internet but I wouldn't know which advice to follow and which not to etc.
If you have money and the knowledge/connections I think it gives your kids a competitive advantage. Obviously, no guarantees (as your size and IQ will impact your goals) but all these former NHLers kids have all these factors working in their favor to help them get to the NHL.