Amazon like Ebay, knows that customers want free shipping. Customers know it isn't really free. They know they are paying the shipping. But they prefer it combined in the price. This has been proven over and over for years.
Another benefit to free shipping on Amazon is the Amazon postage reimbursement never gives you the correct amount for your postage. If you use their shipping settings and Amazon postage; I can about guarantee that you will lose money on postage. Especially if you sell heavier items.
The biggest benefit to offering free shipping on Amazon is you get a boost in search. Amazon will always show listings with free shipping first. This is huge. Ebay does the same thing. And I suspect Etsy will start doing this in the future.
The search for any online venue wants to give the customer what they want to see. And that is free shipping. This is why all listings with fee shipping will rank higher in search.