I've done a little reading trying to get my head around this whole oxygen thing. I'll post what I think I have figured out so maybe some of you smarter folks can set me straight if I'm wrong. Here goes.
Sacchromyces don't need O2 to make beer. They can make alcohol and esters and (mysteriously to me) CO2 anaerobically.
But healthy cell membranes are needed for reproduction, for cell protection, and for controlling what passes in and out of the cell.
Saccharomyces with weakened membranes can produce more esters, more phenols, more diacetyl. They can also have less ability to absorb diacetyl, less ability to resist and survive in high alcohol %, and less ability to attenuate to their potential, or do so more slowly.
They need sterols to build healthy membranes. Sterols are steroid alcohols, and ergosterols are unique to fungus. So, saccharomyces can't build cell membranes from plant or animal sterols but they can get them from dead yeast (like in Wyeast Yeast Nutrient) or they can synthesize them if they have fatty acids (present in wort) and O2 (not present in wort because of boiling)
Yeast that come from a fresh stirplate starter are less in need of O2 because they should have gotten enough from the starter aeration process. Yeast that has been harvested from a finished beer has not been exposed to O2 since the stirplate. New generations created in that beer have never been exposed to O2. The only sterols they have are from their parents or from dead relatives.
Each strain of yeast has its own desired amount of O2 for healthy membrane production, but generally range from 8ppm to 12ppm. With aeration you generally can only obtain about 8ppm of dissolved O2 in wort. To get above 8ppm, injection of pure O2 is required. Also, the higher the gravity of the wort the harder it is to retain dissolved O2.
In summary, if you use fresh yeast from a stirplate, and or yeast nutrient that contains dead cells, and or the beer style doesn't need cleaner esters and reduced phenolics, or doesn't need to fully attenuate or attenuate rapidly, then you can be less concerned about aeration.
If you want to harvest and repitch without a stirplate starter, you might think about your aeration.
If you want a cleaner, or bigger, beer that fully attenuates to that strain's potential, you might want to think about your aeration.
If you don't want to shake 5 gallons for several minutes, or use a pump, or risk contamination from a splashing device and whatever is in the air, or if you need more than 8ppm you might think about injecting O2.
It is possible to get too much O2 in the wort. One symptom could be fusel alcohol (hot solvent flavors). Way way too much O2 could kill yeast as not much lives in pure O2.
But, you don't NEED O2 to make beer.
Am I on the right track?