I sense Netflix worries about the algorithms used by aggregators like Apple TV. It seems like their strategy is mostly quantity over quality, way too much low-value one-season-and-done series to try to keep people hooked.
I don't think there's any 'algorithm' at play with this integration that would concern them. When using Apple TV the search bar will search all the integrated services. So if you search for a movie it'll try and find it on one of the streaming apps you have installed before falling back on iTunes for rental/purchase. The Home Screen also shows the media you are currently watching or have queued to watch at some point. I think from Netflix perspective they want you to go into their app so they can try and keep you there. If they enable this integration suddenly you're launching Netflix content from the Home Screen and you may instead choose in your watchlist that's on another service. As a user, I basically stopped using Netflix because of it. The Apple TV app and integration with services is killer.
But it sure makes it easier to forget about. If someone never watches Netflix, will they keep paying for it? They're missing out on an opportunity to prove value.
I’ve found opposite to be true. Several instances where I was shown only paid rentals via Apple search result but then found I had it available for free on one of my existing subscriptions. I basically lost trust in Apple search results and stopped using it.
Was that streaming service integrated with Apple TV? As the Netflix case shows you not only need the app, but it needs to integrate with the TV app to show in the search results.
Not sure whether its naivete or not, but considering how poorly Apple does at things like search, I'm much more inclined to believe this is just incompetence.