There's more to exams than memorization too, and cheating because you don't like memorization is childish. If the exams really test only memorization, drop the class.
Cheating to avoid memorization is childish, but let's not forget that students are usually children, or still in the process of maturing into adults.
Failing to learn critical coursework should delay graduation, and cheating should result in expulsion. These are good things.
Edit: Being a child, and acting childish is an important part of the life cycle that allows development. We seem to be bumping into some biological limits on how late we can extend it, but if it were possible I would.
There is a tremendous variation between individuals. Part of the point of the university degree as a credential is to identify those people who are responsible enough to complete the program. I graduated at the age of 21 and immediately became an Engineer in Training, working on code that could kill people if it behaved improperly. I took that responsibility very seriously, and I'm thankful that my employer and coworkers took me seriously in return.
I fear that a focus on age tends to lead to prejudice. If you just want to ensure young adults can be allowed to make mistakes without ruining their lives, I would encourage you to expand your goal. There are many adults who could benefit from a bit more compassion and forgiveness. We don't need to restrict it to the young.
Edit: that being said, in a system where there is such a thing as non-compulsory courses, and the critical path to graduation is sane, cheating on an exam on the critical path should definitely not be acceptable, even if it's "only" memorization. Some things really do need to be memorized.