Agreed, Bino's are nice to have, but not necessary to follow general hunter safety rules.
Not necessary, but the reasons to carry optics while hunting far outweight the reasons not to, and they do promote safety.
Say you spot some birds 600 yards away. With binoculars you can verify if there is a gobbler in the group before you spend the next 45 minutes to an hour moving in on and trying to set up on hens or jakes. On public land this is huge as you could encounter two or three other hunters in a 600 yard move, not to mention all of the unseen birds you'll bump. If the turkeys are far enough away (at any distance) that binocs are needed to identify them, your arm movement is not going to be an issue. If you are concerned about unecessary arm movement giving you away, what do you think getting up and moving will do?
A good pair of 8 X 36s only weigh about 20 ounces, 10 x 25s even less, so extra weight is not even worth discussing. As far as cost, what is your safety worth?
I hunt a 450 acre lease in Missouri. From a handful of select locations, I can cover about 90% of the open area on that farm with binoculars. It keeps my movement to a minimum and helps me keep tabs on the other three hunters I share the lease with. In short, binoculars allow me to be a more efficient, safer hunter.
Let's face it, the most dangerous aspect of hunting public land is moving around. Optics can help keep your movement to a minimum and help you to spot other hunters before you wander into their setups. It's a mystery to me why anyone would always take binoculars scouting but not take them hunting. None of these misguided reasonings stand up. It's still your personal choice, but I hope you give these thoughts some serious consideration.