If check in closes 30 minutes before the flight, then boarding has generally not commenced at this time. In general, an airline would know that a particular flight is oversold even before this time, because more people would have turned up. I have a number of times been asked to volunteer.. but I have never been asked to volunteer whilst sitting on the plane. I have only ever been asked to volunteer whilst sitting at the gate. Therefore, the scenario you paint would be extremely rare, but could be necessary. An airline knows if children under 6 are travelling, if people with a disability are travelling, etc... these are just as objective as any other criteria. What the airlines want to avoid is the effort required to take care of vulnerable passengers in this situation.
Your post generally sound like you try to do a good job for your customers, but to suggest that the US carriers in particular that
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airlines try to take care of people in these situations,
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is laughable and I'm afraid very naive.