Because it makes a potential customer's life more inconvenient, so the customer has incentive to not buy Netflix. For example, me. The only reason I have for not buying Netflix is this little thing.
Also,
> Why would Netflix let Apple list all their content in an Apple branded interface as if it were their own
That's not how it works. It literally says "Open in Netflix" or whatever app. All it does is make it easy to search for stuff, add it to your watchlist, and start playing it.
What Netflix doesn't like is that it makes it easier for its customers to watch non Netflix content...which is obviously anti customer.
Netflix refuses to play game, because they want to keep their data to themselves. Apple would LOVE Netflix to integrate into the app.