I hope that you're right, but it's definitely a big assumption on your part that China (and, of course, Chinese culture in general) will naturally head down the path of caring about the environment in the same sense that Western countries and cultures have started to.
There are different levels of scale at play that make very different tactics work in Shanghai vs Vancouver; in the former there's enough difficulty ensuring that all the logistics work to ensure the populace is not starving that other considerations will necessarily have to go by the wayside.
We also have to consider history and cultural forces, which have inertia, whenever we consider social change over time. The western world is becoming cleaner largely by virtue of each succeeding generation encouraging its children to take stewardship of the environment seriously. Even with this tendency, we still pollute terribly.
I'm not convinced that there is much of an environmental shift in Mainland Chinese culture presently, at the very least in the city cores; and if there is, I suspect it will be generations before it's taken as seriously as it is here, which is still insufficient to actually stop bad things - and still undereducated as to what risks are reasonable vs. simply protesting whatever has the right virtue-signalling associations in the current year.
When you say:
> As China becomes richer
...there's an implicit assumption that "becoming richer" is just a natural, unavoidable, guaranteed outcome of the modern world. This is another assumption, and one I fear would be even harder to justify than Chinese culture becoming environmentally focused in a short enough time to matter.
There's no guarantee that resource extraction at the current rate needed for wealth to outgrow population growth is a guarantee. This means there's no reason to assume that the per-capita average GDP or standard of living is going to rise forever, to the point where environmentalism (in the sense that it's often more expensive) is going to become not only feasible, but fashionable. Frugality may overcome the natural human desire to display wealthiness, if the threshold is too high for the average person.
Lastly -
While your solution may very well become the case in the long term, and again, I hope you're right because it's truly the best outcome, we still have to deal with environmental ramifications today, both of past decisions and of decision being made right now. It's probably better to stem the tide earlier rather than waiting for it to just naturally stem itself.
This might mean "environmental protectionism", in the form of heavy tariffs against goods from countries with lower environmental standards and/or poor enforcement.