Landing priorities are set by the Haitians, the UN, and the US, in that order. If someone convinces the Haitains or UN to approve a landing, they land. Otherwise the US turns away flights who haven't arranged ahead of time. This is what apparently what got the French medical flight in trouble - they didn't give notice ahead of time that they were coming (they probably didn't know who to call and took off anyway).

The "Haitain Government" is a headless corpse right now - I would not be surprised if it amounts to some Joe who worked at the airport previously. That may be the highest-ranking you can find at the moment. UN is not much better in the best of times, and they often have too many people "in charge".

Based on flight rates the runaway & takeoffs/landings don't seem to be the limiting factor right now - parking areas are. Also, no loading / unloading equipment survived. Flights even had to bring their own ladders for passengers to disembark at first! Any flight without ladders for passengers or winches to lower cargo gets turned back. Otherwise they just sit in the parking area taking up space, preventing another flight from coming in. And if there's no one on the ground to receive & move the cargo then whatever the plane lowers to the ground just sits there in the middle of the tarmac, as useful as a dog dropping on a sidewalk.

The final report is probably going to reach the obvious conclusion that absolute #1 priority should go to a Seabee battalion, even ahead of medical flights. A bulldozer may displace a lot of tetanus shots on day 2, but by day 5 or 6 the bulldozer probably pays for itself many times over. One of the harbor piers is apparently partly open now: here's another chance for a Seabee team to be a huge difference-maker.

And as usual I expect that next time the report will be ignored, and priority will go to celebrity sight-seeing and tetanus shots, etc, with infrastructure and construction flights only done at night when nobody is looking.