Being from Ohio I will try to explain THEIR logic.
Most of Ohio is flat. The SE part gets hilly but nothing big. Something like 70% of the state is fairly flat thanks to the last ice age. That is their concern number one, bullets can travel long distances more easily in their minds.
Ohio is a small state. Our square mileage is not large, but we are the 5th or 6th most populous state in the nation. This means a lot of people in a small space.
We grow BIG deer here. People from all over the nation hunt in Ohio for our 7 day season. Since we only have a seven day season (for some damn reason) the woods are typically crowded during gun season.
If Ohio were to legalize all rifle cartridges, I think they should expand the season to three weeks similar to Indiana (exact same issues above) so people had more options when to hunt rather than be forced into a single week. Michigan has similar issues but the state has a dividing line for the northern half of the mitten and the UP. Ohio could do the same in the SE part where there are more hills and less population density.