Skimmers are needed because: ?
We do not need an expensive skimmer to manage CO2, not even for the introduction of oxygen. There are cheaper and more effective options for this. If one has one, I hope it must not be used because the natural processes have failed . In most reef systems a balance between reducers and producers is not present and one can use the skimmer present as an aid, but it will not solve the problem.
If CO2 produced by heterotrophs is used up for new photo-autotrophic growth, the oxygen used up by the reducers, producers of that CO2 can be replenished. In this way the water remains saturated with oxygen and the CO2 present in the living room has little or no influence on the water quality.
Only because you use a skimmer, you need one.