I have been wondering about using this lately too.

Why not set up carbon capture units near alternative energy sources? It is certainly not going to be cheap and there are no real economic incentives for it other than hope for future generations. So, I don't know about the political viability considering this would have to be a massive project run by multiple governments.

But, if we put political viability aside for a second and just think pie in the sky here, technically, why not? As someone else pointed out, nature does this too. But those processes are simply too slow for the rate at which we are emitting. So, I think giving nature some help, at least until we have converted sufficiently to renewable is a good idea and may buy us the time we need.