And there would be no reason to motivate them to do so. The shingles vaccine is just a double dose of the chicken pox vaccine. Those who had the chickenpox vaccine, which includes much of the population younger than 17, won’t be targets for it as they age. Those younger than 50 but older than 17 are currently at lowish risk of shingles before 50 and most will age into 50 (so Merck will make their money). Given the low incidence of shingles before 50 the study would need to be very large to get enough cases without an extremely long follow up period. Either way, an expensive study for little gain.
HPV is indeed based on the concept that giving to populations who statistically may already be infected makes little sense. Those with more partners are at greatest risk and those with more partners tended to start younger than 26.
Of course there was the Mom in practice who while discussing the vaccine for her child, questioning the age cut-off, and whether to give it at 11 or wait until her child was closer to at-risk behaviors, volunteered that in her teens and 20’s she had very little risk - her now ex-husband had been, at marriage, her first and only partner, but that now, well over 26 and relatively recently divorced, she’d benefit more. (Thus the no way to know for sure how long it will last was possibly relevant … maybe her daughter might not be at risk until late 30’s and beyond too.)
Some do not induce protection until a child’s immune system is more developed.