The reason you can't tell that the energy of, say, a baseball is quantized is because the energy levels are so close together at that energy scale. In order to see the quantization, you need to look at extremely light objects that move slowly.
If the spacings were much, much farther apart, you might notice that while you can throw a baseball upwards at, say, 10 mph, which allows it to reach a certain height, you can't throw it upwards at 12 mph. Put a little more arm into it, and you can throw it at 14 mph, but not a little bit faster or slower than that. Put still more arm into it, and you can throw it at, say, 17.5 mph.
But yes, I suppose in the real world, you wouldn't be able to demonstrate energy quantization in the case of a baseball, since you'd never get the resolution you'd need. But lighter, slower objects do apparently behave in the counterintuitive way I described.