You do know that you can hand things to the followers?
You have to have them in Follow You mode, then you Trade equipment with them. They will put the equipment on only if it offers higher stats, as determined by their skills not yours, than what they are wearing.
As for a NPC picking things up, they do that, but who knows what criteria they use to decide to pick something up. However, you can drop things near
any NPC and get a chance for them to ask if they can have the item. The fact that the NPC is a Housecarl/Follower is coincidental in this case.