It should be also said that the actual limit is much lower and starts with 30 km.
Even the current best Surface-to-Air Missiles have a height limit of approximately 25 km. Normal combat planes cannot climb for a horizontal speed higher than 20 km. While planes can take a "running jump" by going full throttle upward (e.g. the F-15 up to 30km), they cannot target well and it gets worse with every km going up.
Some powers have the MiG-25, but those planes will be of limited value against targets over 25 km (this includes the SR-71 which is a spy plane and without weaponry). Superpowers may have advanced satellite weapons available, but they need too much preparation, are extremely pricy and are too valuable to send against a target because it tells the others much too much about the capabilities of a nation.
So if you climb up with a stratopheric balloon over 30 km, every nation on earth is practically helpless. I don't need to say that such a stunt would really tick off a nation and is by no means recommendable.