FWIW, my hunting is always done with round chambered, safety on, and I have used the "see-through" covers to take game--no issues, no incidents.
For me, I don't think that whether you chamber or do not chamber a round has much bearing on whether or not you are safe in the woods. Just chalk me up as one of "those" guys who was brought up under the presumption that simply holding a firearm incurred the unlimited responsibility of its use. That being said, I think the overall opinion of most hunters is do hunt by whatever means you prefer so long as it is done sincerely and SAFELY.
"Everyone who receives the protection of society owes a return for the benefit." -- John Stuart Mill
