I like the idea.
People could set a price to their airline (presumably using the same system as the used market - 70% to 160% of CV, and the price can be lowered if it sits on the market for a certain period of time).
Then the airline could get, say, 50% of the income - the other 50% going for merger costs and taxes. That 50% can be used to start a new airline..
Putting your airline up for sale would mean that prospective buyers could get a read-only view of your airline, so they can appraise your cashflow, scheduling, fleet condition, etc, and decide whether it is a good purchase or not...