I suppose it really does depend on where you mark the end point.  I would have to say if someone explicitly puts the endpoint on a runway, then OSRM should route to that runway even if it's disallowed.  This way employees could point to restricted areas and still get a route.

However if someone says "airport" and not explicitly an off limits area, I would hope by default it would select a proper entry point, likely to the terminal.  But yes what nominatim does with a textual search is out of the scope of either the router or OSM data.  Would be nice to guide it to the more likely target.

Incidentally it's not just nominatim that botches searches to airports, likewise when searching for airports with OSM data on my Garmin (mkgmap) it also gives bogus results likely also due to some sort of centroid mapping.  Ideally there's a way that we could solve both...