Why is coasting wrong?

First, coasting is illegal in some countries and US- States and in Europe it would be a reason to fail the driving test.

Second, a driver has no longer full control of the car.

If you drive a manual transmission and coast in neutral you have to rely on your brakes only. You are no longer able to accelerate or use the engine brake until putting in a gear again. And this takes time. Maybe just a second, but one a driver doesn't want to spare in case of emergency. Putting the car in neutral and brake then is also shortening the life of the brakes dramatically. Shifting down properly and use both engine and mechanical brakes is the better way (and don't worry about the clutch, a clutch is designed for that).

P. S. When it comes to automatic transmission I'm no help. No automatics in Germany, fortunately.