Also, if it’s so dangerous, what adult in their right mind would give a time turner to a child so she can follow more classes? She’ll still literally age the same, spend the same time in school. Just have her take more years at school of age wants to learn more, instead of giving one of the most dangerous items ever to a child so she can use it to literally be in the same building at the same time, something easily verifiable by her classmates.
This simplest explanation is that JKR isn’t a very good writer. She came up with an idea “I’ll give hard working and ambitious Hermione a time travel device so that she can take more classes in the same amount of time” without thinking deeply about the implications of allowing time travel to exist in the universe of Harry Potter.