I am not going to speculate as to why but as an example:
The article talks about government funding...this makes no sense, literally none...it is generally accepted that nation states didn't exist until about 3 or 4 centuries after the period in question, and govt finance as it exists today came half a century after that.
The article talks about companies...again, companies didn't exist for another 4 centuries.
These are basic elements of economic history in the period. If you study history, day one of a research course would be...don't read the present into history. This is one of the worst examples I have ever seen (and part of the research course I did was literally looking at the worst examples...this is worse...no historical article should include comments supporting a current political proposal, as this article does...it is just totally inappropriate).
And yes, the Wikipedia article linked is correct (in the sense that this is the generally accepted account). The dynamics of this are well understood: famines, plagues, wars, etc. triggered huge prosperity (and the poorest generally benefit most as always) because the main limit on growth was the number of people growing beyond what productivity/resources could support (this happened again in the 17th century and is why America was populated...so these periods are significant). When lots of people died, there was room for growth.
No, the BBC is not a reliable source of information and hasn't been for a number of years. The article is (unfortunately) quite typical: people have a preconceived notion about what is true, and then gather information that confirms that conclusion. At best, this is an example of an editor who has hijacked the original article...at best (the university attended by one of the authors is, however, not surprising to me). It is important not to confuse information that you want to believe is true with actual reality. I don't think it is particularly controversial to point out that 95% of the population (journalists closer to 99%) have gone off the deep end when it comes to this.
(It is maybe worth adding, the narrative in the article is one of those subjects where some news organisations will just pump endless stories about how the rich are exploiting X or Y. These articles do very well on social media but the fact that they draw the same conclusion about every single event should lead you to ask whether they don't have an "angle". Eliciting jealousy and rage is money in the pocket for journalists, jealousy is a very predictable and bankable emotion.)
I dunno what corner of academy they are from, but in every one I'm aware of, using historically-specific terminology like this in a different period is a major faux-pas.
I don't see any contradiction between the linked article and the Wikipedia article. Peasants absolutely benefited from the shortage of labor, while feudal lords lost power. This power vacuum was partially filled by guilds and merchants who were able to take advantage of the new economic situation. I'm not a historian, so I don't know all of the details, but I don't think the two sources contradict each other.
As for historical articles not supporting political proposals, that may be a faux pas in academia, but I would hope that the people making and evaluating political proposals are carefully studying similar periods in history to understand the possible effects of their proposals.
I do agree with the spirit but all history is really revisionist history and all is in fact re-creating the narrative in current context.