Sadly, the reality is that the majority don't want to make the effort.
For news articles at least, the only way to be shown at the top of the search results is to write your page using AMP: https://searchengineland.com/googles-amp-carousel-working-se....
Edit: from Google's own documentation (https://developers.google.com/search/docs/guides/mark-up-con...): "The Top stories carousel requires that your content be published in AMP".
This is on an Android phone, using Chrome, with a US ip.
News outlets use AMP because they get pushed out of the carousel if they don't. You have the cause/effect backwards.
Looking at my Google News feed, I see articles from The New York Times and NPR listed prominently in the carousel, and yet neither use AMP.
Edit: NYT does use AMP: https://www.google.com/amp/s/www.nytimes.com/2018/09/06/us/p...
The "benefits" shouldn't be used as a factor to rank results either.
I want the best page content-wise for my search. Not the fastest to load with irrelevant results.
Besides what kind of "proof" do you expect to see? All their rankings are hidden behind several layers of secrecy, and it's not like Google will come out and say it by themselves.
Web search is a public resource at this point, and Google is percentage-wise a monopoly on it, so we should dispense with opaque algorithms and behind the scenes manipulations.
It's bad for society and bad for democracy.
They should be forced to be able to explain any ranking, and give their algorithm at any point in time.