Sometimes when I'm flying I'll try to go as high as possible when flying line of sight. Then it's all about piloting skill and very little about the plane.
It seems like the higher you get the plane, the harder it is to tell if it's climbing or descending. It quickly gets very tricky to keep it at a good climbing rate. Unless you have unlimited vertical, but that takes the challenge out of it.
The challenge isnt in the building; just about any plane with half decent autonomy can be flown way above line of sight and outside of the range of most (non UHF) transmitters. And of course, outside of legal airspace in most places.
As I said before, maybe they could do it on a budget, and maybe have a size limit as well. It could also be just a race to be the first to reach a certain altitude instead of just trying to get the highest one possible.
A race might be more fun, although some of my planes will vanish in to the sky in mere seconds if Im allowed to start from level flight. They will lose speed going vertical but starting out at 180 KmH (50m/s), I might not be able to count to 5 before I lost sight of them. You could again impose a budget limit, but the challenge wouldnt be very different from the speed challenge.