I'm not aware of any sites actually banning Drop Shipping, well not yet anyway lol, but welcoming it may be a stretch lol
A site like eBay is more customer focused than they are seller focused, and the term Drop Shipping has been known to strike fear into their tiny little hearts at times. Understanding why isn't that difficult really, for example you (the seller) aren't actually in charge of what you are selling. So here is a recipe for disaster, buyer gets an order they aren't happy with, complains to seller, who then isn't able to assist directly with the problem, rather they have to then chase it up with their supplier.
So when you consider that eBay is customer focused, that's not a recipe for good customer service, which then reflects back onto eBay themselves.
Just list within the regulations on any site, and keep the term Drop Shipping under wraps lol