That for me is where the logic breaks down, a comprehensive vaccine programme for shingles would seem far more effective than just hoping the adults come into contact with infected children.
Anti-vaxxers are a thing. If you vaccinate then due to herd immunity the anti-vaxxers don't get exposed to chickpenpox nearly as much and then end up getting shingles.
Also then anti-vaxxer children get chickenpox much later in life when it can be more serious.
If you don't vaccinate everybody gets exposed to chickenpox much more and the proportion of shingles cases ends up being smaller, not only that but anti-vaxxer children don't need to worry about getting their first case of chickenpox at age 30.