It's a stretch by any measures that embassies must monitor air pollution in order to provide travel advice.
If you really want to bring air quality to the attention of travellers it is of course possible to write "Air pollution can be high" on your country page, no need for real time data (why not also UV, pollens, water quality, then?)
I doubt that "Air pollution can be high" is really enough. I don't think someone living in rural France or Scandinavia is really equipped to understand the level of pollution in a city like Beijing, without more information.
The Danish government actually does write that "Air quality in major cities can be very poor" in their travel recommendations for China, and links to statistics (http://www.aqicn.info/city/beijing/). If that data is any good I don't know, but the US government feels that it need to collect it's own data.
If you really want to bring air quality to the attention of travellers it is of course possible to write "Air pollution can be high" on your country page, no need for real time data (why not also UV, pollens, water quality, then?)