Specifically, the problem is not having a large and young workforce productive enough to support the elderly population.

Observe both the shape and growth trajectory of populations for America, EU, China, and other entities at: https://www.populationpyramid.net. I think a lot of countries are going to have a similar problem - it's not isolated to China. However, China's unfriendly immigration policies, combined with the very large skew in their population demographics (both age and gender) lead many to believe that there will likely be issues like the one I mentioned earlier.