What you should discuss with them is their strategy for using discounts. The feature you suggest is not a bad one, but even if we did have it the choice to use it would actually be up to individual merchants rather than their affiliates.
For the time being though, the only way for there to be no discount code box is if there is no eligible discount that can be applied to the products in the shopping cart, and the only person who can control whether or not that is the case is the merchant themselves.