Most plastics aren't actually recyclable, which is why they aren't recycled. But we say that we can because it shifts the burden. Companies like Coke have been saying that they'll have 50% recycled material in the next 20 years for the last 60. ~~Fusion~~Full recycled product chain is only 20 years away!
Also, 17% of France's energy comes from recycled nuclear (70% from nuclear)[0]
Most plastics can be recycled into energy by burning them, just like "spent" nuclear fuel. The difference is that plastic waste occurs everywhere and collecting it would cost way too much, but nuclear waste collection works very well.
I presume one could, with present technology, incinerate a stream of mixed plastics, collect the CO2, and turn it back into hydrocarbons. I’m not sure this counts as recycling.
"Not recyclable" in the literal sense. You have lower yields when you reform plastics and there's always contaminants which are difficult (read "we don't know how to") remove. This is a complicated technical challenge. In fact, the recent John Oliver episode was on this topic[0]. There's kinda this weird conspiracy about this, which is more about shifting responsibility.
Though the more honest answer is closer to "mostly not recyclable, a bit not economically viable". But that also depends what we mean by "economically viable". If we're using it in the typical sense of "slightly more expensive for producers" then a small percentage increase. But if we're talking about "if producers had infinite resources" then well still no, but we'd be able to recycle a bit more (we're still not talking much more). I'm assuming the former because the latter is an absurd position.
Also, 17% of France's energy comes from recycled nuclear (70% from nuclear)[0]
[0] https://www.world-nuclear.org/information-library/country-pr...