Adjusting the EBB can certainly fix a chain that is so loose that it falls off. Generally you can tighten the EBB a few times before removing a link. When the EBB is at the outer limit, removing a link ought to bring it back near the inner limit. I haven't gotten to that point yet! If the EBB is not near the outer limit, I expect that removing a link will shorten the chain so much that even at the inner limit the chain will be too short/tight.
One fun debate is how frequently to switch chains. A worn chain will push the wear on the sprocket and chainring - that's the theory, anyway. I started out going through a few new chains, switching before the EBB got to the outer limit. But then it seemed that the sprocket and chainring were worn enough that a new chain wasn't fitting so well. At this point I have run out of theories!