I don't want to be contentious. I just want to present a few things as counterpoint:
When water is heated to strike temp and and then the wort to mash temps the O2 concentration is reduced.
Reduced, yes, but not eliminated. Solubility at mash temps is still ~4-5 ppm. The crux of the issue has always been that the flavors we associate with LO, particularly malt flavors, i.e. fresh lingering grain, are tied to one or more of the low weight malt polyphenol compounds (PPO is a likely candidate although there are others) which themselves have antioxidant properties. That means they will be the first in line to oxidize at the DO levels present at mash temps.
That's why it ends up being so important to us not to mash in to oxygen saturated strike water.
And once boiled it is reduced even more than in the mash.
This is true. That's why we boil the strike water prior.
In my mind, this eliminates the ‘hot side’ as a source of dissolved O2. Therefore, antioxidants should not be required here.
If we consider that strike water will have ~4-5 ppm DO if untreated, then I agree with you. Someone not performing a LO mash will have no need for antioxidants.
On the other hand, if I am performing a LO mash, even if I pre-boil the water, I still need a mash antioxidant or a purging system to ensure that mashing in doesn't dramatically increase the DO content and to mitigate the ingress from atmospheric oxygen, i.e. an antioxidant provides a safety margin during the duration of the mash. Depending on how you mash in, you can introduce between ~1-3 ppm DO, and intrusion from atmospheric oxygen can be upwards of 1 ppm/hr.
As far as kegging is concerned, I try to "stay in my lane", as I am a bottler and always will be. I just don't have the knowledge, outside of what i can research and observe from my collaborators, that is required to make compelling arguments for or against those packaging methods.
The big takeaway in my opinion is that for someone performing the traditional homebrew mash (how does NorDO strike you?!) your assessments are accurate.
For the LO mash, however, the initial strike water DO content is paramount and an antioxidant (or grist purging) plus the use of a physical barrier such as a mash cap (or mash "headspace" purge) is important to keep DO levels low prior to pitching yeast.
Just for posterity sake, I should point out that as people progress with the LO mash methods, they tend to significantly decrease (or in the case of those who use purging eliminate) the use of antioxidants. This is due to pre-treating the strike water, underletting, mixing grain and water gently, and capping the mash. Ultimately we arent talking about large amounts of antioxidants in the mash.