I seem to recall they spun PayPal off because a few activist board members and/or shareholders wanted to pad the bottom line, nothing more. It wasn't that bad of an idea in a vacuum because third party payment processors seem to pop up all the time, PayPal was just the first major name in the game and is probably still the most well known, despite the competitive landscape.
Regardless, you're correct that they're never going to compete with Amazon, except maybe in percentage of fraudulent transactions. Bezos is building an empire, eBay is just an auction site with severe little brother syndrome that can't accept excelling at what it used to excel at.