Paid for through taxes? So you want to pay for a new facility with public money to compete with existing private operations? Are you a lawyer??
If it is a private project how will it be paid for? Increased charges to airlines? They may save a bit through efficiency gains from fewer diversions, but I would have thought not enough to cover the extra charges required.
Surely the cost of paying for a new airport will...
....reduce the profitability and that is exactly why some routes end prematurely and many are never started. It also affects the fare price and hence the demand.