You are now talking about the cost of the technology, but that's not the complete picture. Switching to carbon free energy will probably work, but it will take longer to get to where we want to go. If it takes longer to stop climate change, there will likely be higher costs in undoing the effects of it. There are already severe droughts and highly unusual weather right now, if it takes us another 20 years to undo what we've done, who knows what kind of extreme weather we will see?
However, if we can prevent (more years of) extreme weather and rising sea levels by extracting CO2 from the atmosphere, then the total bill for the whole project will be lower because we don't have to pay for undoing the damage.
Additionally, who says that money spent on climate change prevention is money wasted? I'm fairly convinced that these investments will actually create jobs, in addition to preventing disaster.