Costco could benefit from a relationship like that, yes.
Just like Apple benefits from having software like Steam being available on a MacBook despite the fact Apple has a store that sells the same software.
Open ecosystems are a thing.. because they can attract a greater volume of people.
Closed ecosystems tend to make more money per customer; and if you can have a closed ecosystem AND be a huge market leader, you've hit the jackpot (like Apple has with the iPhone.)
Here's a basic way to explain it: I'd be more likely to buy an Apple TV is I could shop on amazon's video store with it.. I don't currently buy movies or TV shows through iTunes because I don't have an Apple TV. I mainly use an HTPC; if I were to buy an Apple TV to then buy things from Amazon, I'd also be getting iTunes exclusive content advertised to me.. and thus, am likely to end up buying some.
Costco could not benefit from letting other retail stores take up their space for free just because Costco charges shoppers a membership fee.
I don't understand your argument.
So because Best Buy is open, it should allow Amazon to open a store inside for free? And Costco should also give Best Buy a free store inside a Costco for free because Costco is closed?
Your HTPC can show movies and TV shows bought through iTunes.
Amazon has already created video apps on iPhone and iPad because it works both ways--users are more likely to use Amazon if it is available on their devices. If not, people are more likely to use Netflix and Hulu.