Rattlers are safer than other poisonous snakes because they give you a sound warning when you get close.
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I did trail maintenance work for 16 years in mountains that were habitat for Timber Rattlesnakes. I can tell you from experience, they do not all rattle! Several, even when coiled to strike because we were hassling them to get them to move on from a work area, just did not rattle (& their rattles were not missing).
For the ones that do rattle, you may still be within their strike zone. What is really scary is to hear one & not see it so you don’t know which way to go to get away from a potential strike - that will get your heart racing for sure!
I agree with every thing you said. Except other venomous snakes make not much sound except hissing. So occasional sound warning is helpful over no warning at all.