Fear of falling is good and bad.
It helps us stick to the rock and finish climbing a route. When you try to finish climbing, you are not learning techniques but performing moves to finish. When you don't have that fear, it is like top roping, just making the moves and improving.
But one should not blindly apply that when performing because you could fall by not paying attention and you can get hurt.
So, work with fear of falling when it is safe. Hang on to your dear life when it is not safe because injuries even minor one like a simple sprain can set you back many months.
Train as if you are climbing. Climb as if you are training.