What would be the challenges to taking off and landing a typical passenger jet at FL300?
These are the main challenges I can think of:


High takeoff and landing speed: To generate enough lift for takeoff in the thinner air at FL300 (gravity has almost not decreased, so required lift stays almost the same), very high speeds are required. Combine this with less thrust from the engines available and you need very long runways. It should still be possible to accelerate and takeoff eventually since FL300 is still below the maximum altitude most jet airliners can climb to (coffin corner).
Tires: The tires used on aircraft have a maximum speed which would be exceeded when taking off or landing. Other tires could be developed, but it is a major challenge to make these work in the cold temperatures (rubber does not like freezing temperatures, that is why Mars rovers do not use rubber tires).
Cold Temperature: It is cold at FL300, around 220K on average or around -50°C. This is not only problematic for the tires, but also for fuel, which would be constantly close to its freezing point. A heat exchanger between e.g. engine oil and fuel would be mandatory to operate an aircraft from here.
Wind: Wind speeds can easily reach 150kt at FL300. The runway would have to be perfectly aligned with the wind to have a pure headwind component. Otherwise, the crosswind would quickly exceed the limits for the aircraft.
Engine Failure: FL300 is above the maximum altitude for OEI (One Engine Inoperative) flight, which implies one cannot return to this airport after an engine failure. An aircraft would be forced to drift down to a normal airport for landing.