I don't think RFDS will nudge Angel Flight out.
The reality is RFDS is a quasi commercial organisation that only flies when it gets paid either by government or donations. It actively competes against commercial organisations behind an umbrella of a charity.
And before anyone yells unfair, RFDS does a great job but it's tentacles reach beyond its original scope of operation.
As Angel Flight mostly operates on the good graces of us fellow pilots donating our time and basic aircraft cost, RFDS would not be a party to flying what amounts to a flight that doesn't at least earn total operating costs.