Just for fun, I'm going through my ancient games. Who? Never heard of? Vanishville?
As a kids trainer I of course know that only a tiny percentage will become "professionals" (and I merely mean that they play for our team of adults, not that they earn money). Is there solid data on the concrete amount (which of course locally varies due to size of the club, available trainers, social milieu etc. pp)?
The best indication I can come up with is: how many kids playing rated tournament chess are still playing rated tournament chess 10 or 20 years later?
Out of 145 players in a junior USCF tournament I selected from late 1996, 17 of them have played a USCF game in 2007 or later. Only 7 of them have played a USCF-rated game since 2017. That's about 12% and 5%.
For comparison, out of 30 players in an adults-only competition held at the same location at the same time, 20 have played a USCF game since 2007, and 11 since 2017. That's about 67% and 37%.
As a kids trainer I of course know that only a tiny percentage will become "professionals" (and I merely mean that they play for our team of adults, not that they earn money).Is there solid data on the concrete amount?
The simple answer is "No" because the question appears to be carefully constructed to NOT have any meaningful data.
If you has asked about the percentage of children aged under N playing FIDE rated chess who are still playing FIDE rated chess N+m years later then that could be answered.
Here in England there is data available to organizers and arbiters regarding children's dates of birth which could be used to suggest some kind of answer but that data is problematic.
First, it is not available to the general public because it is open to child protection issues. So, there is no way of independently verifying any results.
Second, it does not include data for children who never played an ECF rated competition. That probably already excludes a significant number of children.
Third, playing for an adult team is a very variable bar. In our club we have had at least one (adult) player play for a team with an ECF rating under 1000 and we currently have adult players playing for lower level league teams for us rated about 1300. I don't think those examples would count as "professional" in any sensible definition of the word.
