one of the reasons you cant take them is because of the invasive mussels and fear of them being spread even more. also many of the mussels in ohio are endangered and it can be very difficult to tell the differences in some species. the shells you see in streams could be from people using them as bait but many of them die off naturally and minnows are incredibly good at cleaning off shells.
if you wanted to eat them dont worry freshwater mussels are disgusting, the only reason they are havested is to make buttons, fake pearls, and pig feed
See Judoka's link above. Descent article about why the mussels should not be disturbed, or shells kept. What it boils down to, is that there is a commercial market for the shells but there are several endangered species in Ohio that are difficult to i.d.. So, a blanket law was passed to protect them all.