I'm not by any means saying it is not desirable to raise pH that is 7.7. I would raise it. That has nothing whatsoever to do with O2.
If all the air run through the skimmer is recycled over and over, how could the skimmer possibly add O2 to the tank? Where would it come from?
Reducing CO2 in the air does not increase the O2 content in the air by any significant extent.
As for folks claiming they have plenty of other aeration, they may need to think again. Only a reef tank that showed zero pH swing day to night can claim perfect aeration. many reef tanks become O2 deficient at night, and I personally would run a skimmer even if it did nothing but aerate the water.