Kinda reminds me of how some older people would pick up their prescriptions at my Dad's pharmacy and tell him "Don't give me any of those child-proof caps. I don't have any children at home to open them for me."
The Optum RX mail-order pharmacy has caps where both sides can be the "bottom" and screw onto the bottle, but one side is childproof and the other is just a normal screw attachment. Since they come with the childproof side of the cap engaged, this does present the bootstrapping problem of getting the bottle open to begin with, but thereafter you can just use the other side of the cap.
But again, it's like the other OP said: The childproof side is the one that they put on first which could present an issue for older people. I'd imagine you could ask them not to do that, though. I never really thought about it.
https://upload.wikimedia.org/wikipedia/commons/3/31/Walgreen...