Honestly, the situation where it'd be fine to carry a barrel without any problem would be like Bag of Holding or Tenser's Floating Disk (or other conjuration spells), but that would be employing a Magic Item or a spell just to move one barrel, and the Disk likely could be spotted by enemies, which means the player is using a resource and is actually engaging with mechanics and is strategizing with the barrel instead of just picking up 5 and going to town.
Which would make Barrelmancy actually include casters and be a limited strategy instead of something that can be done constantly by anyone like it is now.
