I think the missing piece here is the core charge, which makes the average user think of the battery as something of value that shouldn’t just be thrown in the trash. Currently, I think a lot of users with an obsolete phone with a smashed screen would just throw it in the garbage.

It's not the core charge that makes you return a battery -- it's the core refund.

Agreed. The point of the core charge is to make the program more palatable to manufacturers. They’d rather the customer see the charge as a line item than rise their prices to fund it. I think the line item also helps educate the customer at purchase time that the refund exists.