If we had this option, we could "sell off" (destroy) worthless items at a vendor that we have clicked on. This would allow us to rid our bags of worthless things more rapidly. For example, if I go to a vendor and click on an Intricate Bloodpact Boots armor piece that I have acquired, I can click "sell" to destroy it, rather than learn it's worthless after trying to sell it, then have to re-click on the boots, then click "destroy".
I think we'd be more likely to get items that are just vendor trash being marked something like "treasure" and then getting a Sell All Treasure button.
That wouldn't address my concern for ridding ourselves of tradeskill items we have made etc, but that would be a good feature as well.