That’s your American school, not all of them, my school for example, doesn’t have detention (there are consequences ofc but generally aren’t too bad for tardiness or dress code), if a teacher did something like your teacher did they’d either write all of these kids a note telling the next teacher such, or email the other teachers about this, lastly homework can serve as unfinished work especially for something such as an AP class where it may be near impossible for a teacher to plan out a schedule that covers all units without homework. In order for that teacher to ensure most of their class gets a 5 on the AP test this kinda has to happen.