I pick up street litter, and having picked up thousands of pounds, I have never felt that loose caps are a problem, let alone one that requires such a solution. The number of littered bottles, with or without a cap, is greater than the number of loose caps, and the amount of plastic in every bottle dwarfs the plastic in a cap. Fixing the cap to the bottle will do nothing to improve the recycling rate of plastic if entire bottles are already tossed anyway.

I consider the idea of cap tethers as adversarial memetic warfare thrust upon us for some unknown ulterior purpose, possibly to make us hate the very idea of environmental consciousness. Same as paper straws. I like plastic bag bans though.

As far as picking litter is concerned, I personally prefer finding bottles without a cap. At least those are empty, all liquid having evaporated after the bottle has spent several months in the bushes. The capped bottles are often half-full and are just nasty. (Who even pays for a bottle of drink and not drinks half of it anyway?)