So the computer picks 8 people, and you call out the first four on the list. One of them refuses, just like what happened here. Now what?
Your solution just has the airline crew going, "Fair enough, sir, you can stay" and then calling the next name. At that point, the next person knows that refusing is allowed, so he does too. Pretty quickly, you're absolutely going to be on a flight where five of the eight refuse, and now you're back to bludgeoning elderly asian people. And at some point, the whole system becomes public knowledge, and you now add the element of fights between passengers because we all know that only four of us get to refuse.
Or you just eject all eight of them and four can later reboard. Again, what if one or more refuse.
There is a solution in place already. United just didn't choose to employ it. United offered vouchers to anyone who wanted to voluntarily give up their seats. They reportedly bumped the offer one time. They didn't bump it enough. There's your solution. I promise you everyone on that plane had a price. You can find four people who'll take say $2000 to miss a flight to fucking Louisville. Does United think $2000 is too much? I guess so, but at that point, United has a problem that can be solved by effectively buying back some seats, and sellers get to set the price they'll take. It would have been a hell of a lot cheaper to have paid them.