It may not be such a burden if
there aren't many different types of items to deal with. But still, I don't know what items will be in the games apart from gears and weaponry...
Avoiding trash items as potential valuable items would be nice. Like, you could find an empty bottle on the floor and keep it for throwing it at an enemy's face, like a disposable throwing knife or something. But as you know these are no value in shops, you won't keep that in your inventory very long.
Items like empty bottles, bricks, broken pipes, dead rats, torn clothes, snooker cues, and whatnot... these things shouldn't have any use in crafting also. So you may just bother about them when you're in need for improvisation. I hope at this point that crafting will be more technologically advanced than "tape a fork with a stick and it makes a club" kinda crafting.
One problem with delivery drone would be A.I. pathfinding, and to some extent, having to define by hand every zone where the delivery system could or couldn't move to.
Another (possibly fun) issue would be the exploit of calling the delivery system to take cover behind it, or exploit it another way to your advantage (collision bugs, or whatever). But if that feature comes in by the player's need, it means that this potential exploit is available at any time in the game.
About the car's trunk, I think we shouldn't count too much on that unless the car is indestructible, or the items from the car are virtually sent up to the basement (so they aren't physically present in the trunk). If the car's blown up or something, it shouldn't be fair that you lose some precious or (worse) unique items that were in it.
Like you said, these were just plain examples so I don't mind much the consequences of them and enjoy the creativity in solving the inventory issue