Nobody but the USPS is allowed to put anything in or remove anything from a mailbox.
If you're talking about a separate locker, not a bad idea but I'd assume that would be a lot more costly than replacing your lock and also would introduce all sorts of variability about size and where it would be placed.
Yes, or a strong-box that interlocks with a closed exterior door. Amazon's no longer content to just metaphorically want access to our homes and lives, now they actually want in..
If you're talking about a separate locker, not a bad idea but I'd assume that would be a lot more costly than replacing your lock and also would introduce all sorts of variability about size and where it would be placed.