Even open book exams can be gamed. There are whole industries set up around enabling in-exam communication (e.g. concealed subvocal mics/headphones) and outsourcing schoolwork.

It is definitely possible to design assessments on which cheating is difficult. For example, oral examinations or personalized per-student projects or exams. The problem is that this style of personalized assessment fundamentally does not scale past a few dozen students in a classroom.

You want a classroom that small, it's going to cost you. Just instructor salaries for would run each student 10-30k per year, and that's before paying for infrastructure (classrooms, tech, offices) and (admittedly not always useful) administration.