The Netflix app has always been treated badly by Apple. No idea why, but it means that I can’t have Netflix content in the “What’s Next” queue (among other things, like Netflix actors’ work not showing up in show information).
Netflix refuses to play game, because they want to keep their data to themselves. Apple would LOVE Netflix to integrate into the app.
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.
Why doesn't the macOS App Store game search include results from Steam? That would be a very consumer-friendly thing for Apple to do, right?
The answers to both questions are related.
It is purely an inconvenience to Netflix’s customers for the sole benefit of Netflix.