That's just my experience. If a customer
pays for a new gizmo, they want the "latest and greatest". If it doesn't look latest and greatest to them, they feel slighted. I'm not saying it's necessarily rational, only that it's the way customers on average react. They don't always say it directly, but word gets around. I've seen it many times. Humans judge books by covers.
As far as old-looking sites like Ebay, if an Ebay competitor appeared with equivalent services and product choices, yet LOOKED fancier/stylish, Ebay would start to lose customers. Lucky for Ebay, no such site exists. (If they appeared, Ebay would probably spend on a visual revamp.)