Sometimes you have to end your shopping trips early, because you get encumbered by huge bags and simply can't carry any more.
Stores don't like when this happens, because customers who would've kept buying things go home instead of continuing to shop. Customers don't like it because they're stuck
carrying huge bags the rest of the day.
Why not have a system of home delivery stations all over the city (I'm thinking walk-in booths near each subway stop -- called "Shopmore's"), where people can go, drop off their bags, and say "please deliver this to 277 East 5th St", and when they get home their bags will be waiting.
Shopmore's could be subsidized by the major department stores. If many stores agree to collectively finance Shopmore's service, then it will be free for all customers to use and may be mutually beneficial to the stores, too, as it encourages more shopping.
In reality, Shopmore's delivery may end up being free for items you've purchased at a sponsoring store, but pay-per-item for items you've purchased at an independent store or just general items you'd like delivered.