Just stating it does not make it a fact. Your conclusion is in error.
If from now on you have to sell 100 because of this type of behavior, even if not overbooking, in case you have to accommodate your employees, etc (exactly this situation), then you get $20,000.
The $2000 loss gets eaten by future customers in more expensive airline tickets. What other explanations would you like?
This is why your math is in error: they didn't "get" $22,000, they collected $22,000. There's $22,000 of contingent liability attached to that. So the most they can book as income is $20k plus whatever no show fees they may collect. That's a market transaction and I have no problem with that.
But there's the $2k contingent liability that has to be satisfied before the remaining $2k can be booked as income. They have to buy their way out, bump to other airlines or flights, etc. So that $2k will not be booked as income until that's satisfied, and that will cost.
Selling the chance to take a flight is not the same as selling a flight. If they're not acknowledging the difference up front, that's fraud.
That's why your math doesn't work. Now, let's go to the idea that overbooking as a policy in general and involuntary bumping as a practice is unethical, immoral and should be illegal.
If it's simply a dollars issue as you say, treat it as such. No involuntary bumps. Keep raising compensation until you get the volunteers needed. But disrupt their life with an arbitrary bump because it's cheaper? That's just wrong.
BTW, I work in the transportation industry. Flight crews are strictly limited in on/off duty time. Did you know, for example, that if a flight crew lands at an airport on an overnight stay, they aren't off duty until they reach their hotel? Timing out of flight crews happens more often than you might think. So I understand the need to get a fresh flight crew somewhere so you don't have a cancelled flight. My objection to this situation wasn't the bump but the arbitrary, involuntary nature of it.
I do not care if there are economic benefits to others. It's immoral, unethical and wrong, wrong, wrong. At some point it will end. Sooner would be better.