I think there's a fundamental misunderstanding about how these systems work in 2019.
There's not "an algorithm" that can be published and inspected, like good ol' Pagerank. It's probably more accurate to think of it like thousands of slightly different algorithms knotted together, tied to an enormous database that selects with algorithm gets used for which person at which point in time. The knot and the database are constantly changing.
You could perhaps publish the machine learning algorithms that created the recommendation engine, but those won't tell you anything useful without the training data (which, for these systems, is absolutely huge and complex).
I'm convinced that a big reason these social platforms haven't fixed their recommendation engines is that they actually have no idea why they recommend the things they do.
The systems are trained on "engagement", without regard to whether it's good or bad, happy or sad, constructive or destructive. It's just: which thing collects the most clicks from which people.
In a way, this makes these recommendation engines mirrors into human nature--which sounds cool, but is actually boring and banal. We already knew that it is easier to make someone unhappy than to make them happy. And we typically want people to build things that deliver happiness--even though we know it's harder.