You are 100% right in that this is the primary mechanism for increasing the standard of living around the world. It's worked so well in fact that the wages in China are not nearly as low as they once were. I would say that low wages alone are no longer the primary benefit of having something made in China. It's much more the scale and loose environmental regulations that are valuable now. There are quite a few things that you use every day which are almost exclusively made in China or India or similar.
I think people in general do not realize just how much we rely on China and Chinese manufacturing, and how beneficial it is for everyone to have things made abroad. People focus on the higher end factory items like iPhone assembly but don't often think about all the sub-components. Base materials like adhesive, spray on preservatives, plastic containers, labels, etc. are almost all made in China or somewhere with loose environmental regulations. There are so many items that go into day-to-day items that are either made in China or made from products imported from China. If it's made from plastic or for plastic, and it's made at scale, there is a really good chance it's made in China.