It's not really taking them higher than they would "normally" fly. Wild falcons often fly high and that is a learned behavior. Height is an advantage -- they can see more area and they're less likely to be spotted by prey.

The issue is about training. Pretty much all our medium and large falcons (peregrines, gyrs, hybrids) are captive bred, so humans are the only thing teaching them to fly strongly and hunt. And because we're humans, we want to train quickly so we can go hunting and nail some ducks.

Climbing to 1000', 1500' takes muscle, and all the techniques (balloon, kite, drone) give the bird motivation to get up there and build that muscle. It also trains in the habit of getting to a good height.

The ultimate goal is to train the falcon to wait on: to circle high above an area where there's game. The higher the pitch, the height at which the falcon circles, the larger an area the falcon can cover. While the falcon waits, any game in the area will be pinned and reluctant to move. That lets the falconer control the field, have their dog flush the game in a specific direction, and be in a good viewing position for the take.