Amazon is set up MUCH better than ebay. It took me ages to get a refund on something that I had to return from ebay. If they had better things put in place to protect the buyer and the seller, then ebay would be great for buying 2nd hand things, but amazon does a much better job at protecting people.
Amazon has too many irons in the fire and can't even keep its employees happy. Amazon has a tough road ahead and it is very unlikely that they will put eBay out of business. eBay is a great auction platform and while they've made decisions for themselves that have harmed their business model I don't think they're in danger of closing up shop.
Ebay is an addiction for a lot of people. While Amazon's marketplace sellers are abundant it is a totally different market of purchasing. Chasing an item on Ebay is nowhere near the same as hitting the buy button on Amazon. For that reason alone I do not see how the scenario would ever be viable.
The reason I think that Amazon will probably not put Ebay out of business is because Ebay is a very popular and widely used shopping site. Although Amazon is on par with Ebay because a lot of people use Amazon as well, I dont think that it will completely put ebay out of business. Also Ebay can sometimes be a lot cheaper than Amazon