As someone who is (formally) a postdoc it seems that the points raised in this article seem to apply mostly to postdocs who are not (formally) postdocs.
That is, indeed, there is no such thing as a "post-doc". But in most academic institutions, there are non-tenured researcher positions - fixed-period or otherwise - which have a Ph.D. as a requirement. They may called something like "Researcher", "Research Engineer" or "Research Staff Member" (as opposed to "Academic Staff Member").
Of course, my knowledge is as anecdotal as yours.
In my field (math) and country (USA) there are many postdocs.
Maybe you are in a different field or country?
(If you really don't believe me try search "postdoc" on math jobs https://www.mathjobs.org/jobs?joblist-0-0------
They add the term "post-doctoral" to indicate that you need to have completed a Doctorate. Or if you wish - to indicate that the conditions will be poor :-(
This was at another well-known US school. Perhaps thing are different in Britain, but I am not aware of any R1 university in the US where postdocs "do not exist."
My view is that there is a problem in academia where people in non tenured positions are being taken advantage of. However, most of these people do not actually have "postdoc" in their title. Positions with postdoc in the title are typically reserved for people who just received their PhD. It is fairly difficult to get a tenure track position directly from a PhD program, so (most) professors were (formally) a postdoc at some point in their career, and it is an important training step for applying for tenure track. (I hope this clarifies my above point, sorry if it was unclear).