I mean, think about it. The resource can (and will be) cached. Does it make any sense to also cache ephemeral links with it?
Then why are the single most important and widespread form of resource links, HTML URLs, always included in the response body i.e. in the HTML document itself?
There's a reason why HTML is primarily used to provide human-readable documents, while web APIs are implemented based on other document formats that are better suited to provide machine-readable resource encodings.
Hyperlinks are one of the basic semantic markup tags. They allow machines to read them and insert jump points. The key here is that they are machine readable to enable behaviour that wouldn't be possible otherwise.
Unless you've held an election, you only speak on behalf of yourself and yourself alone. If you're having a hard time understanding basic concepts then naturally it's unlikely that you'll have an epiphany in a discussion where you're decided to take an hostile stance towards details you're not understanding.
Meanwhile, you can ponder how these specifications you're claiming you and those you claim to be representing don't understand are actually used extensively, and it's such a basic concept that it even features in intro tutorials to REST APIs. Perhaps that's a good sign that basic concepts such as web linking aren't that complex or hard to understand as you've tried to assert they are.
So once more: sure we can do things your way, but why is it better? Every other source says link headers are an option. You claim they're superior. Why are they better?
Why does representing links in headers and not bodies make the API easier to understand, navigate, or use? How does it clarify the interactions? What do I gain from it?
So far, all you've said is "relationships are metadata" or something, which is not how most people consider relationships, and even if it we're true, it doesn't explain why my response can't contain metadata, as long as it's marked as such.
Aside from that, I'm curious how do you manage alowing API clients to create new relationships or change them?
What's hard to understand? If you add a resource then you update your link relations. If you actually tried to implement a REST API instead of RPC-over-HTTP then the client navigates link relations just as before. That's pretty much the whole basic premise of REST.