I think learning basic chess is a good idea. It teaches a valuable idea very cleanly: The duality of offense and defense. This is a very valuable idea and not just applicable in violent war, but can also be applied to business and some competitive social relationships, including things like organized sports. I see a lot of people who lack this basic concept trying to operate in environments where it is crucial to understanding what is going on around you.
In my opinion, going deep into it like this into chess specifically has rapidly diminishing returns once you understand that concept.
However, there is also arguably some value in just putting in the effort to learn anything to that skill level, and childhood/teenage years are a good time to do it because you have the time (witness those in this very conversation talking about trying to combine it with the university time of their life... many people have learned how bad an idea that is the hard way....); chess is merely one of a panoply of possible options. It's probably not my personal first choice, I'd tend to suggest musical instrument mastery or language mastery or something else a bit more generally applicable, but if it floats you or your child's boat, that's fine. It's a lot easier if you have some buy-in.
I would just make sure to include an out; it's really easy for parents to encourage something and neglect to inform their child that it is a valid option to put a reasonable amount of effort into something and then move on when they're ready. My parents, 100% accidentally, did this to me with community youth baseball. In hindsight, they basically did nothing wrong, they were trying to be encouraging and supportive and everything else, and it just never crossed my mind to say that I didn't really want to do it, and I mean no criticism of them. But it was a blinding revelation one day when I realized that I could just not do that anymore.