Historically, this model grew because the journal publishers provided the necessary infrastructure to print and distribute copies of the articles.
I am one person watching the world go by but I think that there was, is, far too much emphasis on things that can be counted.
People became afraid to make subjective judgements of quality. They demanded data. So whatever was the thing they counted, it got maximised. Quality is a slippery concept and it is harder than counting.
Judge scientists by the number of papers they publish, and they will publish a lot. A manifestation of the quantifying fetish.
Not all academics support it and several groups have opted out, publishing in open access only or organizing their own journals and conferences.
It really seems like it's the inertia of existing administrators that haven't shifted away from judging papers based on the prestige of the journals they get published by.
Once the prestige factor goes away, and authors are judged primarily on the quality of their work, the publishers will lose their stranglehold.
Of course, that means a lot of entrenched interests losing revenue streams, so it's going to be a long struggle of grassroots change vs regulatory capture combined with reactionary pushback.
Having those journals owned by publishers that engage in rent-seeking behavior is.
"Prestigious" is completely arbitrary and heavily lobbied for by the publishers.