1. the big oil companies and the massive political machine that supports them drops the whole "global warming isn't real" line, no more snowballs being taken in to congress and all that. Because now they can just say they'll suck it out of the air and they can continue to think they can keep burning all the coal and oil they want (which of course they should not). Once everyone is on the same page that global warming is real, they can't go back on that. If the approach here proves to be insufficient (which it probably is), a lot of political points have been scored in any case.
2. the machinery to suck out the CO2 is another big "green" industry, like solar or wind, but doesn't compete with oil/coal! it's meant to mitigate the damage they do. So as you've noted, way more money and attention might end up going here, increasing the chance of its viability.
3. No matter what happens with the rate of burning oil/coal, we need this anyway. There's consensus that we're pretty much over the point of no return with warming due to all the ice that has melted, and if the permafrost goes that might be catastrophic.