puberty blockers are used explicitly to delay having to go through puberty. they are used for kids who have precocious puberty (puberty that starts too early), as well as for trans kids. there are some marginal risks associated with them, you might grow a bit shorter, or just generally develop differently that you might have if you had allowed puberty to progress on time, but there aren’t specific health challenges people who use them face. the reason you take them is to explicitly prevent somebody from going through irreversible changes they might not like before they can make an informed decision, or before it is healthy for those changes to occur.
interestingly, most of the poor health outcomes of precocious puberty are psychological and social, not physical, which is, i think, an interesting parallel to the trans experience.