As I see it, the fundamental issue is that they're trying to create some kind of hand-made artisanal solution to a problem that is already being addressed on a vast scale by industry. My plastic waste is collected at the kerbside and has been for over a decade. It's baled up and sent off to a facility with huge automated sorting machines. Why would I take my plastic waste to a workshop when the local government already collect it from my doorstep?
Precious Plastic have designed various DIY plastic processing machines for what is essentially hobby use. That's fine, whatever, but for about the same cost I can just buy a commercially-made machine. A manual injection molding machine or a benchtop filament extruder is just a thing you can buy on AliExpress. If you wanted to set up a half-serious plastics business, you could buy an old Boy or Arburg injection molding machine on eBay for close to scrap value. If you want to feed that machine on recycled plastic, reprocessed pellets and regrind are a cheap commodity product.
The problems that remain in plastic recycling are mainly really complex engineering and material science problems, because re-melting inevitably degrades the quality of polymers. Those issues are being slowly chipped away at by serious researchers in academia and industry.
I don't doubt their sincerity, but feel-good aspirations rarely solve much of anything.
A lot of comments here seem to assume that the goal of PP is to provide a complete solution for the plastic waste problem. It's not and it doesn't have to be. I may be off base a bit but I think the amount of plastic that is actually being recycled is only around 10% on average (with substantial spikes in both directions if you look at it on a country basis). So there is more than enough headroom to do something useful with the stuff that would otherwise have been burned or buried.
I kind of sort of agree with your points about the manual machines but Aliexpress was not as prevalent as it it is now 10 years ago and it's not as if there were already lots of open source blueprints for injection molders, extrusion machines and the like (unlike for example in the 3D printing space), so the knowledge built up and shared by PP is still useful.
I guess it's also a pretty human thing to want to tinker with making your own machines and share them (if not, there also would not be a bajillion static site generators, notes apps and whatnot in the software world).
I don't really agree about your points about the industrial injection molding machines, though. Sure, if you want to produce many of the same parts, that's ultimately the way to go. However, if you want to do small-series stuff, experiment with different ways of making molds, do educational hands-on stuff and so on - which is what PP is much more about than maximizing output - a manual machine is much more appropriate.
Anecdote: I regularly had people from (university) departments who have all sorts of professional injection moulding equipment use our - in comparison ridiculously primitive - setups. Because it was much easier, much faster and the "vibe" in a Precious Plastics lab is usually also very different than in a research lab (and that's also not to be underestimated if it's more about development/experiments/learning than about maximizing output).
Also: Fucking around with old hydraulics can be a rather dangerous activity and requires some safety considerations not relevant in manual machines.
I can't speak for your locale, but in the US, most "plastic recycling" is a myth, as very little of it is truly reusable. Trash companies basically resell what they collect, and if they can't, it ends up in the same landfills as the trash bin contents.