Right. The solution is for them to immediately say: We need 3 people to take this offer of $800 in US cash (not vouchers), or 3 people will be selected randomly.

I guarantee there will be enough takers. The issue is, even though the cost of overbooking is already factored into the cost of the flight, the airline is still trying to eek out extra dollars by offering less than the cost (vouchers, starting with lowball offers, etc).