Because no matter how much the price for direct air capture (DAC) falls in the future, it's still going to be massive. The submitted paper estimates a current cost of between $94 and $232 per ton. That's a big drop from a decade ago on a per ton basis, but it's still massive overall. At the low end you're looking at a minimum of ~$1.34 trillion annually if we were able to capture 100% of the 32.5 GtC of emissions accumulated in the atmosphere in 2017 alone. That's also completely ignoring the total ~230 GtC of the same since 1870 as well as emissions absorbed by the land and oceans (which has its own negative effects).
Nobody expects to remove all of it, or even all of what we'll continue to emit via DAC. Just keeping the expected increase to under the 2°C degree upper limit agreed to in the Paris Agreement is going to be challenging in itself even with cheaper, more efficient DAC methods. Actually reversing the temperature changes would be the "dream" for climate engineering. Something like that--which would involve every type of carbon dioxide removal methods along with atmospheric and space-based solar radiation management--would be a herculean project on a scale the human race has never before attempted. It'd make the Apollo program look like a five year old with a lemonade stand. And eventually, we'll have to figure out a way to make real progress on that front.
Basically, the hope that climate engineering will allow us to fix it later--or better yet, the dream that we can reverse it altogether--is both appealing and potentially dangerous. Why sacrifice today when we'll figure it out tomorrow? Just look at US infrastructure spending for an example of that kind of thinking.