Hmm, I'm not really sure I understand the logic behind the narrative that the authors are putting forth.
What's getting in the way of the production of great 'non-purified' philosophy that the authors call for? As they point out in the article, it used to be the case that "philosophers could be found anywhere — serving as diplomats, living off pensions, grinding lenses, as well as within a university."
If they still can be found in those places, then that sort of undermines the narrative of the article.
If they can't be found in those places these days, why not?
Perhaps they can be found, but they aren't being given due recognition by the Powers That Be in academic philosophy departments? Why should that matter? Many great philosophers in the past were rejected by the academics of their day. Some of them had their books banned (Descartes), faced political exile (Locke) or were excommunicated (Spinoza), so it seems to me that the non-academic philosophers of the past faced far greater challenges. Moreover, the authors lament "philosophy’s contemporary position of insignificance in society and marginality in the academy." If institutional philosophers are so insignificant and marginal, then how could their lack of recognition of the non-purified philosophers matter very much?
Maybe the idea is that our wider culture (not just academic philosophers) foster an idea from an early age that 'philosophers' are academic professionals, so people with a proclivity towards philosophy all feel pressured from an early age to follow the 'purified academic' path rather than considering alternative ways to pursue their philosophical interests. But that doesn't sound very plausible. At least in the USA, there is very little exposure to philosophy, so where is this wider cultural expectation coming from? Many people who discover an interest in philosophy either do so on their own, or are introduced to it through college and (occasionally) high school courses. But those introductory philosophy courses typically focus on the great 'pre-purification' philosophers who the authors admire and don't give students much of a sense of what contemporary academic philosophy is like (which is ironic, because then students go on to complain that philosophy is too obsessed with historical figures like Plato and Kant instead of making progress like the sciences. It seems there will always be people complaining about PhilosophyTM, no matter what we do.)