Site owners just aren't going to be excited about stealing the most important bit of real estate and putting buttons there that navigate away from your site, that the end user presumably chose to navigate to. And other problems, like breaking bookmarking, no SEO benefits from the "link", etc.
The selfishness of it is obvious if you think through what would happen if someone posted one of these dig iframed urls to another digg-like site, which was then itself posted to a third digg-like site. 3 stacked headers, yay!
I'd think that too, but site owners were perfectly happy to go with Google's AMP for a while (maybe still). They put a big "X" to close out of the article and go back to Google in a bar at the top as well as horizontal swiping to get to other versions of the story at other publishers.
I agree that site owners shouldn't like this behavior. Still, we've seen cases where content owners have welcomed things against their interest in the name of engagement or hype.
For example, a lot of video producers started putting content on Facebook (where they received no revenue) because they were getting lots of views on Facebook compared to their own site. This eventually left them without the revenue they needed and they dwindled.
Yes, site owners shouldn't like these kinds of things, but we've seen sites chase a lot of crazy trends. The Oatmeal has a cartoon that kinda sums up some of this: https://theoatmeal.com/comics/reaching_people.
Even today, you'd think brands would want to move to ActivityPub where they could run their own server and actually have control; you'd think influencers would want to move to ActivityPub where they wouldn't be beholden to Facebook looking for money to boost their reach or Musk's arbitrary moods. Instead, so many are sticking around on platforms they know are looking to gain an advantage over them. I'm not even suggesting abandoning those platforms, but cross-posting to ActivityPub would mean building a future you're more in control of.
There's a lot of platform behaviors that aren't good for sites that many sites end up being enthusiastic about.
The selfishness of it is obvious if you think through what would happen if someone posted one of these dig iframed urls to another digg-like site, which was then itself posted to a third digg-like site. 3 stacked headers, yay!