It would not hurt, but this just makes no (economic) sense currently, and that's not gonna change any time soon.

Right now we don't have any CO2 scrubbing process without significant maintenance or operating costs, so this would add significant cost to all those ACs. Furthermore, the effect is marginal: With emissions of >6 tons of CO2/year/human, you would have to scrub a lot of air (>10m³/min with cost-free 100% efficiency, which is a pipedream) to compensate (for a single human); running the ACs on full flow all the time might not even be worth it depending on how efficient the scrubbing is and how clean the source of electricity.

You might say scrubbing clean 10m³/min of air for every human sounds kinda feasible, but just compare the realistic cost of such a setup to the options that are currently implemented, and how much popular resistance/feet dragging they already meet (renewables, nuclear power, electrification, CO2 taxation).

As a general benchmark, I would suggest that before the scrubbing technology in question has not managed to be installed at most major stationary sources of CO2 (coal/gas power plants, etc), it is not even worth discussing it for distributed air scrubbing.

You have to start somewhere. Even a not great solution can set the president, with goals to gradually increase the efficiency. Mandates can do a lot — just look at the catalytic converter. Put it on all HVAC systems and _something_ will happen even if a small effect given the HVAC itself is contributing way more CO2.

We need all across the board solutions, and if you start requiring small scrubbers to function that can start to provide scale effects that can translate for bigger systems.