Here you go :
https://www.morebeer.com/articles/how_yeast_use_oxygen
Pretty much answers the question.
Thanks for pointing out this excellent summary. It is important to separate the two very distinct functions oxygen performs in yeast metabolism. If one could get past all the recent screaming of "Crabtree! Crabtree! Yeast doesn't respire!" it would become quite clear why actual, practical experience demonstrates that a starter on a stir plate, exchanging CO2 for O2, produces a far greater mass of far healthier yeast, leading to better ordered fermentations, better beer, and yeast better prepared for repitching, and why it is important to decant the liquid containing undesirable products no matter how you grow your starter. Common sense may come round yet again. (Standard disclaimer, YMMV, it's all a crapshoot with homebrew.)
I just haven't found your concerns to be anything other than theoretical. I have found non stir plate starters, pitched with the starter wort to make beer that is at least equivalent to what I was doing before. There's common sense, and there's practical experience. YMMV, but again I think you're painting with too broad a brush.
I was referring to the line of arguement I've encountered that "since yeast don't respire, a stir plate couldn't
possibly help, so you shouldn't ever use it" while there's plenty of published and practical evidence to the contrary. This explains why. Continuous gas exchange can improve growth and health, and it has nothing to do with respiration. So it can be useful, but that depends on lots of other aspects of your process. I personally rarely use a stir plate, my starters are usually too big, so just O2 at the start. But I'm still in the camp going for maximum cell count and long term health, because I'm not pitching at high kräusen, just doesn't fit my brew schedule. If you are, then you can't decant, so you want to avoid excessive aeration of the starter to avoid pitching off flavors with your yeast. If you plan to repitch, other concerns are involved. There's no single optimal method, but no wrong one either. The article provides insight into some subtleties than can help you decide on what aeration practices best suit your own yeast handling and fermentation procedures. I think it's a good resource. I'll have to reread it at an earlier hour of the day, saw that post on my way to bed.
I like Jim's point a lot. There are two models here, as there are two stages of yeast growth in breweries: lab propagation, stepping up at high kräusen, and brewery propagation, successive completed and decanted batches. The "vitality starter" follows the lab model, the decanted "starter" the brewery model. Distinguishing between the two, with their different goals, would eliminate confusion about the "right" way to conduct them. FWIW I have always personally referred to my procedure as "propagation," not a "starter." But in general conversation that subtlety gets lost.