"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.
[0] https://www.youtube.com/watch?v=Fiu9GSOmt8E
