The problem is people who just want to bag Whitney for bragging rights and don't feel any sense of stewardship for the mountains. I think it's exactly the same as what I have read about all the trash on Everest, just 15,000' lower.
Any sort of deposit that required going back to the Visitors Center to redeem the deposit wouldn't work. Whenever I've come down from Whitney or the Cottonwood Lakes trails I haven't got down to Lone Pine until long after the Center is closed. I would hate to have to choose between losing a substantial deposit or staying overnight.
The only thing I can think of that might work would be to station a ranger almost 24 hours right at the Zone boundary to check for wag bags. If people who didn't have a bag were fined the maximum amount the program might pay for itself.
