Think about it in terms of cars. Imagine spread out 3k cars around the surface of the earth. Each car will be thousands of Km away from each other. For example New York has 5 million registered cars. And they manage to use only a fraction of available land dedicated to roads. So I don’t think 3k is anything for a orbit around earth, which is also much bigger than the surface of the earth itself

Edit: I am not saying a collision would not cause the effect that OP referred to. I am saying that 3K satellites in Earth's orbit will be very far apart, so the odds of them colliding in the first place is incredibly low.