Excellent link by Scion on SiliconInvestor about plastic pyrolysis and recycling and the issues.
It's cost prohibitive to sort garbage for the plastic needed. The pyrolysis plants mentioned have that same issue. I understand that it seems like a no brainer to break down plastic into fuel since waste plastic is thrown away and therefore free. The logic would seem to say if they can be 10% effective then it's better than nothing but that's not the case because the cost of obtaining the plastic from the waste stream is a huge problem.
"However, the Reuters review found some advanced recycling companies struggling with the same obstacles that have bedeviled traditional recyclers for decades: the expense of collecting, sorting and cleaning plastic trash, and creating end products that can compete on price and quality with fossil fuels or virgin plastic."
That cost also applies to pyrolysis. There are some technologies which could reduce the expense of sorting plastic but if that's cheaper then recycling will still be the most value adding alternative. If diesel becomes more expensive then it's because oil is more expensive and, as a result, the price of scrap plastic which is made from oil will also go up. Pyrolysis is a no-win situation.
The math is easy and shows plastic pyrolysis can't be profitable.