There are a lot of items and weapons that benefit unarmed strikes along with tavern brawler that are innately hindered by the inability to do unarmed strikes while having a weapon equipped. Monks have a work around but that's limited to their bonus actions. The flawed helldusk gloves are uniquely tailored to let the wearer swap between damage types, if you could choose between the attack types. If the Custom Bar would lock in the unarmed strike and weapon strike that would be an easy fix, but as soon as you equip a weapon the unarmed strike is deleted from the custom bar.
Just keeping it in the Custom Bar or on the common actions would be an appreciated quality of life improvement.