The fact that Anne's mother is as unlucky as Anne explains why Anne is so blithely unaware of her misfortune. She would have grown up in a house that was already prepared for Anne-level bad luck, and she would've seen herself as normal because she was just like her mom. Anne isn't stupid or oblivious...she's just a well-adjusted teenage girl living what she considers to be a normal life.
Also keep in mind that several of her accidents should by all rights have killed her; the fact that they don't means that she's justified in thinking that she's lucky to be alive.
Botan's low self esteem fits into her poor-health shtick...she's suffering from depression, i.e., poor mental health.
Clinically depression is defined by a lack of motivation, though, and Botan has no problem with that. Tanaka from the same season and studio would be closer to depression, and even that it isn't really the case.
Correcting bad luck is nice and all, but what are these kids going to do about college? Sure, in some cases (e.g., Anne) you could argue that improving her fortunes is more important, but is it really worth sacrificing your career to correct your bad sense of direction or tragic love interest?
The opening of episode 8 implies they do have normal classes; just the happiness trainings get mentioned because of Law of Conservation of Detail. And as for Hibiki... her No Sense of Direction is practically a disability that needs to deal with; in the manga Ren once said Hibiki was once lost her way for a whole seven hours between school and home.
