A fine doesn't cause immediate harm as you don't have to immediately pay it while you challenge it in court, having your IP or website blocked happens immediately and will continue harming you until it's decreted that it wasn't lawful.

That depends on the country you are in. In some countries you have to pay anyway and then you get it back if you win the court case. And they're banking on you not challenging the fine because the fees for the court case will exceed the fine so you lose either way.