It is illegal for Amazon to shove deliveries in the mailbox.
Your mailbox is only for USPS to deliver mail and put mail in and anyone else putting mail into your mailbox other than USPS is doing so illegally.
Amazon cannot place any packages or deliveries into your mailbox and instead Amazon delivery drivers must only leave the Amazon deliveries and packages at your door.
I once had a few packages placed in my curbside mailbox from Amazon when my driveway was iced over and although it was not legal for them to do so, I can understand why the Amazon driver did it.
It was no big deal to me and I really don't care if they do, but if it was reported to USPS they could get into trouble for it.
For me although the mailbox is considered postal property, it's also my mailbox and I have no issue with it.
But normally most Amazon drivers will not place any packages in your mailbox as they know it's not legal.