MCAT is a standardized exam and the conditions are very stringent - it makes sense to have it this way because you are directly comparing applicants on a national scale.
Take home exams are often very different than simple multiple choice tests - they are often open ended. Furthermore they work differently for different classes - they don't work too well for cut throat pre-med classes (but this is a generalization and I have had science classes where I had take home exams). The culture of cheating really depends on the environment - some environments are more laid back, grading is less harsh, professors are looking for more critical analysis rather than "right or wrong", and in these cases take home exams work fine. Some environments are really high-pressure (ex. top pre-med feeder schools), and maybe it won't work so well here. There are students at every school/class that cheat, but certain elements can make the cheating more widespread or more contained. Furthermore, cheating can be discouraged by raising the stakes.
I don't know where you are getting confused - are you projecting?
Are you thinking that take home exams are simple multiple choice tests? In my experience 99% are not. Every take home exam I have gotten for a science class has been very open ended and outside research was not only encouraged, but needed. Collaboration was needed as well for take home group exams (yes, this is a thing).