This is exactly what Apple attempted to do, but Netflix never provided API access or data, so Netflix shows never appeared in the unified interface.

That would be great, with the caveat that if a service cannot provide content for your account, it will not be shown in the search results.

Prime is the worst offender of this, but having Crave and Bell TV app installed on an AppleTV means any search returns a result, but you can't watch any of them without buying another subscription to a "channel" they offer.

This is what amazon prime does.

True. But it only solves half the problem. Or to put it another way, their particular implementation just leads to a different frustration. So Prime aggregates content, which is great. So I can browse a great meta-catalog of content from various services. The problem is I'm not subscribed to all these services. So I scroll through the catalog and find something interesting, but... you need to sign up for a monthly plan to watch whatever show on whatever service. It might be a little more palatable if you could pay (a reasonable amount) per show, or series or movie, or whatever. But as is, it's just an exercise in frustration. I'm not committing to a subscription to watch one show that happened to seem somewhat interesting.

Netflix actively fights against these integrations - both on Apple TV and on Google/Android TV they refuse to integrate with the APIs that would give you this exact experience.

They also tend to refuse allowing their customers to watch on platforms they don't like - e.g. they actively blocked casting to Google smart displays and blocked Netflix app from working on Macs and Vision Pro so you can't download things.

Then Netflix should not be shown in such an app, and people will wonder why they bother paying for it if they find themselves using it less.