I don’t know what % of plastic the cap comprises in a plastic bottle but I bet its double digits. So annoying as it is to use, attaching the cap to the bottle does make sense for recycling. It also lessens litter.

But it needs to be paired up with a deposit refund scheme. Lots of countries do this already and encourages circular economies - the soft drinks companies purchasing recycle material to reuse. I bet those schemes measured a significant jump in recovered plastic when virtually all the caps come back with the bottles.