The CO2 footprint per capita in the United States is 15 metric tons [1], so at 300M population, that's 4.5e9 metric tons of CO2 per year.
At 1 metric ton CO2 removed per day per tower, we would need 4.5e9/365 = 12.3M such cooling towers. Even if the efficiency increased 2 orders of magnitude it is still not enough, and I doubt there is a need for even 123,000 cooling towers.
None of this is to say that it shouldn't be pursued as a business opportunity to sell CO2 to commercial customers.
But realistically, given the scale of the CO2 problem, we still need to dramatically reduce the amount of CO2 we are emitting per capita as a primary measure, with any carbon capture as secondary.
1. https://data.worldbank.org/indicator/EN.ATM.CO2E.PC?location...