We should do that too, but then the question becomes what to do with the carbon. It turns out that getting rid of it in a safe way is a pretty difficult problem. The solution that's described in the article needs a lot of freshwater and the right type of rock for it to flow through so it can't be done where most of the power plants are located.

That leaves basically two solutions; capture the carbon from the air, which takes a lot of energy, or ship it with tankers. The first is being done (at a small scale) and the second is being worked on.

In an ideal world, we wouldn't have power plants that release carbon, but that's another discussion :)