Small plastic pieces used in Case 2 (Bottle caps & tear offs) can find a use beyond that of a lid for plastic storage. Lego pieces are probably the most famous product case of small plastic pieces that are designed in such a way to elicit play when joined together.
If plastics are to find a second life after their use in portable storage, then there needs to be an incentive to reimagine what their use could be in a different context. Since bottle caps and tear-offs can't be remoulded after their initial use, perhaps they could be designed in such a way to serve multiple purposes after being used as a package cover. Designing them in bright colours and inventive shapes may make for nice desk toys or playthings for children.