I haven’t used BJU Press Spelling, but thought I’d respond! I know some people do choose to move their kids who don’t have spelling struggles to something more independent after a few AAS levels, while others use it all the way through. Some also combine kids in a level to make it easier to teach multiple students.
Many children have trouble spelling in the context of their writing, especially if they don’t have a separate editing time. Often they are not ready to put all of the skills they have learned together in outside writing until closer to junior high. When students are writing outside of spelling time, they have many more things to focus on–content, creativity, organization, punctuation, spelling, grammar, capitalization, what kind of audience they are addressing–it’s a lot to think about at once.
So, students tend to need a lot of help with this no matter what you use. You might find this article on how to handle spelling mistakes helpful.
HTH as you decide how to proceed for your kids. I hope you find something that’s helpful and works well for your family.