I've started picking up amazon deliveries at local shops (Collect+). This is working out rather well - no need for special lockbox or a supersize ring o' keys.
They really need to expand this a considerable amount. I'm not against the idea of giving keys to Amazon, if done in the right way. More ideally, I'd have an electronic lock that could grant them access for particular orders.
A lot more convenient than when they (luckily rarely) decide to drop the package to the local post office, which is quite far away and closes early.