I think it can make sense in specific cases.
For example:
I live in Boston and a bunch of people don't have cars. If you don't have a delivery service in your building to take and store your packages, they can be left right outside the door which is kind of dicey, especially if you have valuable stuff.
Some people at my office just have all their packages delivered at work, which makes sense. But if you are going to have a ton of stuff delivered, or heavy stuff, it can be a hassle to then lug that back to the subway whereas it might be easier to have it delivered to the 7/11 that is just a block away from your place.
So like I said, it has specific uses. My guess is that the incremental capital spent isn't much to have the locker system, so why not test it out. Low risk - high uncertainty bet on Amazon's part.