People pay more for the 16 flavors of Colgate because they want to pay more for Colgate… that higher price means more margin for the retailer. By eliminating the higher margin products in an already low margin business, you are basically making the situation even worse.
The only reason why generic brands at stores can end up being high margin for the retailer is because the retailer has literally used their market position to start manufacturing cheaper versions of high margin products on their shelves. Unless NYC want to start manufacturing dryer sheets and toothpaste, that’s not an option for them.