Bio load (metabolic weight grams) in aquarium is very important.You can calculate your fish bioload and compare biofilter media here
https://aquariumscience.org/index.php/7-3-media-volume/
Some scientists have already made research and experiments to understand efficiency of protein skimmers ( This singular piece of equipment is typically the second largest expense after the tank itself and it is important product for market )
Protein skimmers are like antibiotics also removes beneficial microflora and beneficial nutrients. When someone see brown gunk in collection cup more than half of it is dead beneficial population in water column.
https://www.reef2reef.com/threads/protein-skimmers-doing-more-harm-than-good.693422/
As for air exchange in PS just airstones in sump and open water surface of tank O2/CO2 balance can be maintained this also helps PH balance.
Healthy, mature reef tank houses enough TOC consuming organisms to effectively keep TOC levels at some acceptably low equilibrium level without the intervention of a protein skimmer.
Protein skimming (bubbles) removes approximately 30 – 40% of the bacteria in the water column of carbon-treated or organic rich water, but the remainder is not susceptible to bubble-based removal.
It appears likely that some types of bacteria are indeed “skimmable”, but others are not. Thus, skimming inadvertently provides severe (?) evolutionary pressure to skew the tank’s resident water column bacteria population to favor the “non-skimmable” cohort.
The skimmers typically removed greater than 80% of the BSA. In contrast, perhaps one of the more interesting observations to emerge from these studies is the fact that all four skimmers tested removed only 20 – 30% of the total organics present in authentic reef tank water.
https://reefs.com/magazine/the-deve...ve-evaluation-of-protein-skimmer-performance/
https://reefs.com/magazine/further-studies-on-protein-skimmer-performance/