1. How much additional energy does it take to pulverize the rock?
2. What about the effect the rock will have on soil pH?
3. What about leached salts and heavy metals?
That is limestone, the article talks of basalt which seems would require more.
Fortunately, rocks can be crushed with power from solar panels. There remains the issue of whether those panels are better used, just now, to displace natural gas burners emitting new CO2 than to crush rocks to absorb CO2. Or, equivalently, if NG-generated power used to crush rocks makes more CO2 than would then be absorbed by the rocks.
In a near enough future, it won't matter, because the NG will all have been displaced already.
I'm way more concerned with the side effects of the process as others have mentioned. Maybe not heavy metals, but soil PH, and other poisons.