What you’re suggesting is called a CO2 scrubber, and is an **outrageously** expensive piece of technology that pretty much only sees use in industrial filtering applications and airtight environments such as spacecrafts and submarines.
Pulling CO2 out of our atmosphere for something as trivial as fizzy drinks when there are many chemical processes that generate a ton of CO2 just as a byproduct does not make economic sense for anyone.
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