Taking off from the highest altitude is not efficient for combustion of the aircraft. So, there will be longer runways than usual ones.
It means it costs a lot to build a new airport in mountainous places.
Especially when it comes to mountainous ones where it's difficult for us to access by rail, road, or ship, the remaining transportation mode is only air.
But, because of the reason above, it's not cost-effective,compared with ordinary airports.
Then, it would be important to precisely calculate costs of each transportation mode before building a new airport.