Have you ever heard any school starts in any month, and ends in any month?
How can the teacher guarantee that your child learn all the necessary stuff to survive in chess tournaments? The teacher in fact has not system at all, or at least has no clear plan for what to teach. S/he may just grab a few classical games and teach your child some tidbits. Of course every tidbit has nutrition, but does your child get the maximum benefits of chess? No one knows.
How can s/he measure your child's progress? There is no objective standard, only subjective opinion. We all know subjective might be twisted or sugar-coated.
Giving parents an easy way to quit actually will increase quit rate. If the child hits roadblock, or has a busy schedule, s/he will ask to quit. And the parents will not persist because they have an easy way out.
The reason for us to align our class to school year is that we want to mimic the education system for other subjects, such as math or English. You sign up for a full-year course, and you make the commitment. Commitment is important, because chess is not a 3-month project, instead a 3-to-5 years long term project. For some, it might be a 10-year project. Starting with a non-committal attitude will most likely lead to non-committal ending.