Given that a coal generator produces 20 g/s of CO2, you could have fifteen coal generators running at 100% uptime before you max out the 300 g/s consumption of a single carbon skimmer. Realistically, nobody runs that many generators constantly. A smart battery and an automation wire are too cheap not to include in a generator setup. You simply can't overproduce CO2 without a lot of oil based infrastructure.
Polluted oxygen also isn't too big of a problem, in my opinion. Sure, it's annoying to have a few pockets floating around, but a few deodorizers should mop it up fairly quickly. Plus, it's still breathable, free oxygen. A tip: instead of dumping into a cave, using a liquid reservoir surrounded by chlorine gas will get rid of the germs in the water, meaning you can filter the water without worries. I had a lot of fun building a chlorine tank for my last base, along with an automation loop to allow clean water to be pumped back into the system, and it was a closed loop, meaning it only cost the 10W power drain of the liquid shutoff allowing the cleaned water to exit the loop.
I'm slowly coming around to using polluted water instead of clean water in my early thermo aquatuner loops. I still need more practice setting up my temperature exchanges for geysers, but practice makes perfect. I plan to tackle optimizing the output of a natural gas geyser to run a 100% uptime dual generator setup, with a single priority feed line drawing for cooking. I'm debating whether it's more efficient to cool the natural gas from the geyser to 40°C before or after pumping. Cooling before pumping costs less resources, but I worry the low thermal conductivity of natural gas will risk overpressure on the geyser before I can cool the previous cycle of gas.