Why do the cities pay for them? Why aren't the coal-burning energy utility companies paying for them, out of pocket?
Because no-one has the power to make them, I think. If it's easier (and probably cheaper) to take measures to address the problem yourself than it is to force compliance, then that's the sensible way to go.
And that's even if they can correlate them properly.
With the right connections you can get away with ridiculous crap, but rules as written are not that friendly. Which creates lots of problems for small companies.
Wealth disparities are always going to allow for corruption, aren't they?
The State in China explicitly picks winners and losers from state companies (in particular banks), tightly controls currencies, tries to resist movement of labour, and attempts to hide moral hazard through censorship. All the while guaranteeing full employment.
But some of the key definitions of capitalism is quite entrenched in the society:
- means of production are privately owned
- profit-motive
- market-driven economy / competition
- inequality
- minimal government interference
China definitely does not fit all the hard-core capitalism definitions, especially the minimal government interference part, but it's closer to a capitalist economy than a communist one.
Lastly, no, the state does not guarantee employment, that has not been true for at least 30 years.