Although his details are likely correct, this is not an analysis from physical laws (and other hard requirements, eg usability requirements) which is what you need to show optimality, it's an exploration of the known options.
He makes the point that labs wouldn't adopt a cheaper machine - yes, much cheaper processes are often adopted first by outsiders, who couldn't afford the current ones. Not clear if there's a huge market for home PCR or similar (many DNA-active chemicals need to be used under controlled conditions because mucking with your DNA causes cancer -not sure about PCR specifically)
From a physical point of view, I wonder if energy- transfer thermal cyclers could be replaced by adiabatic compression, which is likely much faster. Depends how well these enzymes work at high pressure. Could be problematic at a process level though.
one of the coolest parts about the original inception was the application of taq polymerase. veritasium did a video of about it not too long ago. a friend of mine and a man whom i very much respect was mullis's lab manager at the time.
A PCR machine is a lot like a lathe or a milling machine. The price of the machine is absolutely dwarfed by the tooling and consumables.
This is about modern PCR, which is already optimized a lot compared to early PCR. And if you're in a "normal" lab, everything around the PCR, all the handling and preparation will be such a large chunk of time that improving the PCR time alone doesn't really matter that much.
In a very automated, high-throughput setting I'd imagine that parallelizing the PCR would be the best way to increase throughput. There probably isn't that much potential in speeding up the time compared to just multiplying the number of reactions. Which is part of the point of the article.
Regarding the cheaper lab instruments, I'm not quite convinced by these ultra cheap examples. Many lab instruments need quite a bit of precision and reliability, and I would be suspicious that the cheap examples here could compete in that regard. Even PCR needs pretty exact temperature control across many individual reaction vessels. Of course the margins on lab instruments are likely enormous, and there should be plenty of potential for cheaper ones. But I don't think the ultra-cheap DIY stuff will convince people, and it'll likely also fail at the purchasing process anyway for larger institutions.