You can. In West Europe we have been doing that for decades and the lower SOx levels compared to the US and China show the result. Over 25 years ago I visited a coal power plant which used filters to get rid of NOx and SOx. A by-product was plaster which got used by the building materials industry.
But can you filter CO2 without spending so much energy that it's basically pointless? Particularly here, I notice climate change quiet a lot during last decades. Weather, especially during winter is nothing like it was 20-25 years ago. In China population is much denser, therefore effects are more noticeable. Also they are not nearly the worst ecology offenders. If China created as much pollution per person as US, it would be much worse than it is.
You are confusing two completely separate issues:
- CO2 is colourless and largely harmless at the ground level. In fact a modest increase in CO2 makes plants grow faster. CO2 is a problem in the higher atmosphere where it acts like a greenhouse, reduces the earth's heat loss, and makes the Earth warm up.
- Smog and acidic rain damage to forests and cities are the results of sulphur and nitrogen oxides, resulting from burning dirty fossil fuels, and burning under such extreme conditions that atmospheric notrogen becomes oxidised.
When I was a small child in 1950s London smog was awful, and killed large numbers of London's weaker citizens each winter. The problems came when there was fog, and the sulphur and nitrous oxides dissolved in the water droplets, resulting in a thick yellow acidic atmosphere - this is smog. They passed a clean air act, banning the domestic use of dirty coal for heating and demanding improved industrial pollution control, and within a few years the air in London became fairly civilised. Since then power stations across Europe have filtered much of the sulphur and nitrogen based gases within their flues, and the output of these acidic pollutants had dropped a lot. Low sulphur diesel fuel has improved diesel vehicle pollution a lot, but the higher temperatures in modern highly turbocharged small capacity diesel vehicles can cause a lot more atmospheric nitrogen to be turned into nitrous oxides, and we've seen various scandals related to cheating on that front.
Sulphur and nitrous oxides from industrial systems are only present in fairly small amounts, and in many cases there are simple ways to catch them in liquid or solid form. CO2 and water and the dominant results of most combustion. There is a lot of CO2, and its basically carbon ash. So, its not the most reactive of materials to be able to chemically catch it, and it doesn't dissolve in huge quantities. Most proposed carbon dioxide grabbing schemes have centred on catching and storing the CO2, but that's tough. Nobody has successfully demonstrated a practical way to do that on a large scale. There have been various attempts (try Googling for carbon dioxide sequestration), but they've pretty much all shut down in failure.
By the way, some of the worst pictures you see of terrible city air in China are due to fine dust blown hundreds of kilometres from arid dusty countryside. Other cities were plagued by rapid construction, without dust catchers covering the towers during construction. They use nets to catch most of that now. Other cities are plagued mostly by combustion related pollution.