They've averaged ~13% growth year over year since 2008, doing 16 billion last year. Not sure what your metric is but I hardly think that qualifies as, "worst run brands ever."
This astonishes me. I can't think of any good reason for this except for lack of competition. Among everyone I know almost no one ever buy stuff of ebay anymore and the only people I can think of who use it are mostly scammers.
So, an app that lets you buy anonymously? Brilliant! Really! Just give your payment info to one site that you trust (because its all about trust and nothing else); they buy (maybe in bulk; maybe at a price break) FOR you.
What exists like this now? What market would be best served by this? Is your app in to YC yet?
Well it's a good thing you're not an eBay stockholder. I use it probably a dozen times a year to buy hard to find stuff. Stop thinking the world is you and your friends times a billion.