You ever been in a plane? Ever notice, particularly when you're down low, that things like the buildings you are flying over seems to zip past you, but things further away, like the clouds way in the distance, seem to be moving much more slowly? That's because how fast things appear to move relative to you is determined by how close they are. So let's say you're in a place and you look out directly to your right. Something may be ten degrees in front of you (or 80 degrees from dead ahead), but if it is close, then the plane is soon going to move past it and in only a short time it will be ten degrees behind you (100 degrees from the front of the plane).
But something way in the distance that starts out at 10 degrees in front of you will move a much smaller amount, say only one degree, in that same time.
So, if we have something that is very far away, like the horizon, then going a little bit higher in the sky won't make much difference. I found
a calculator where you can enter the height above the ground and it will tell you what angle you have to tilt your eyes down to look directly at the horizon.
A person standing 1.8 meters is technically above the horizon, but not by much. They have to look downwards at an angle of 0.04 degrees. There's no way a person can notice that without some instrument to measure it.
Put that same person at an altitude of ten kilometers (just a little bit higher than the 30,000 feet you mentioned), and the angle you have to tilt your eyes downwards from horizontal is only 3.2 degrees. That's a tiny amount, and even though it's more than at sea level, a person still isn't going to be able to determine the difference without equipment to measure it. Even from the height of the ISS, about 400 kilometers up, the horizon is only twenty degrees or so below horizontal. That's still easy to miss.
For comparison, a standard 50mm lens on a camera has a field of view of about 45 degrees, so even taking photos from a plane you'd hardly see any difference.
Your ball analogy fails because of one big flaw. The earth is about 13,000 kilometers. If you get a shot put, that's about 13 centimeters. So going from sea level to 30,000 feet on Earth is the same as going from the surface of the shot put to 0.01mm above the surface. How much of a change in what you can see of the shotput do you expect to see by doing that?