All of your arguments are based on the assumption that an over-capacity situation which is only discovered after boarding is common and easy to manufacture.

Also, remember that the compensation for voluntarily yielding one's seat can be "paid" in non-transferable flight vouchers. Airlines don't issue cash for that, and airline employees already have free-travel privileges. To get the right to cash compensation you need to be involuntarily denied boarding, and IDB "pecking order" is not under the control of the agent at the gate.