There are several ways to store CO2 underground, of which the mechanism you describe is one. There remain issues with getting the CO2 from the places you describe to geologically suitable locations.

Above and beyond it, what you’ve described and the high cost of doing it, this is what we end up with:

Fifteen CCS facilities are currently operating in the United States. Together, they have the capacity to capture 0.4 percent of the nation’s total annual CO2 emissions. An additional 121 CCS facilities are under construction or in development. If all of them were completed, they would increase the nation’s CCS capacity to 3 percent of current annual CO2 emissions.

Those percentages are small in part because CCS is generally used in sectors that have the lowest costs for capturing CO2—such as natural gas processing and ammonia and ethanol production—and those sectors account for a small share of total U.S. CO2 emissions. Almost all CCS facilities recoup some of their costs by using the captured CO2 to force more oil out of partially depleted oil wells.