I understand what you are saying. It's not hard to imagine parents or kids asking a lot of questions about the different styles of wrestling at first. I would like to try to persuade you with another perspective, though.
Please consider that:
In singles tennis, the inside vertical line is out-of-bounds, while in doubles the outside vertical line is out-of-bounds.
In track, during the 100m dash the fastest time wins, while in pole vault the highest height wins.
In swimming, during the 200m butterfly the fastest time wins, while in the 3m springboard dive the highest score from a panel of judges wins.
In gymnastics, if your feet touch the ground because you fall of the balance beam then you incur a large penalty, but during the floor exercise your feet need to remain within the designate mat space on the ground.
Within many sports, we have different events. And often events have very different rules and scoring practices. Most people accept such differences because that's the way it's always been.
Imop, the actual reason some people prefer folkstyle is solely because that's always been 'american' wrestling. But I feel people will become acclimated very quickly if like other sports, wrestling became more multi-event related with fk, fs and greco all occurring within the existing american high school and college season.