The problem with predicting that China won't catch up on GDP per capita with the West is that the West too went through those growth phases about a century or two ago. It will take a 100-200 years, but China, and the rest of world will catch up. Just a matter of time. A long time no doubt. But it will happen.
It's easy to grow very fast when you are starting from a very low base. Especially when you are chasing someone.
It's a bit like China's GDP per capita. If it continued growing at the same pace as between 2000 and 2020 it might have had a chance to catch up with US in a few decades or so from now. Certainly Western Europe.
Yet based on current trends they will never close the gap (then again who knows what will change in the next 10-20 years or so).
Of course demographic collapse is not that far either. US and Europe at least have immigrants propping them up.