While the ball is in free fall, yes, the net force it exerts on the ground is roughly independent of its height above the ground, and is independent of its speed.
However, you are interested in the force between the basketball and the ground while the ball is colliding with the ground, and that is entirely a different matter.
When the ball is colliding with the ground, its speed drops from a very high speed going down to a speed of zero, or to a speed going up if it bounces. That means that the acceleration of the ball during the collision, points up. While the ball is falling, its acceleration is down, and that acceleration changes directions during the impact.
Further, since the duration of the impact is very short, the acceleration is extremely high. If you drop the ball from a high height, it will be going very fast when it strikes the ground, and this also means the acceleration is very great. Thus, a ball dropped from higher exerts the same force on the Earth while falling, but a higher force during its impact because its acceleration is higher during impact.
If a ball falls at terminal velocity, there are two significant forces on it: gravity and air drag. The force from gravity is unchanged. Gravity still pulls the ball down and the ball still exerts and equal and opposite upward force on the Earth. However, the force from air drag pushes the ball up, and the equal and opposite force from the ball on the air is down. Overall, there is zero net force on the ball. If we consider the atmosphere and Earth excluding the ball as one system, there is zero net force from the ball on that system as well.
When a ball moving at terminal velocity hits the ground, it will suddenly pick up a huge acceleration that it didn't have a moment before. This means there will be a big net force on it that wasn't there a moment before. The fact that the net force was zero before the impact does not mean the impact itself occurs with zero forces at play.