There are two ways to get someone to do something he doesn't want to do - pay him to do it, or use force.
United chose the latter. That's unacceptable.
Everything else is just bullshit that is being slung around in an attempt to defend this choice, and it can be safely discarded in a discussion about whether the choice was or was not acceptable.
There's obviously a limit to how much an airline could afford to pay for the seat they needed - but that limit is determined by how much they want the seat, and if it is reached, the seat should stay in the possession of the passenger who has occupied it. That's how a free market works - Person A has an item that person B wants. Person B offers payment for the item, and if person A values the payment more than he values the item, a mutually agreeable transaction takes place. If person B instead obtains the item from person A by the use of force, he has committed a crime.
To illustrate with totally made up numbers, if the cost to UA of their crew-member not being able to fly is $1,000,000, then they can maximize their return by incrementally increasing the offer of compensation until either one of the passengers decides to accept it; or the offer reaches $1,000,000, at which point it's cheaper to simply live with the fact that the crew member won't be able to fly. At no point is it necessary nor reasonable to use force.
They rented the seat to a passenger. He (and any of the other passengers) can decide to sell his tenancy (or not) at whatever price is offered. Of course it is unlikely that there won't be a passenger who is happy to relinquish his seat for far less than the amount UA stand to lose by not having access to it; But if so, then that's the way it is.
It doesn't matter why UA wanted the seat. It doesn't matter what the detailed results of them not getting that seat might be - all that does is set the upper limit of what they should be prepared to offer, before they give up and simply don't fly their crew-member on that flight.