corporal punishment does rely on fear to an extent. Speaking as a psychologist, all punishment relies on fear. Personally I have no problem with the idea that a child who has misbehaved, or who is contemplating misbehaving, should be afraid of the consequences of that actual or potential misbehaviour. I hope they are.
But what you are claiming is that this fear is constant – and that isn’t so in a school where corporal punishment is used properly, and in most schools, where it is used it is. A child who has not misbehaved or who is not contemplating misbehaving has no reason to be afraid – and the vast majority of children are not afraid of things when there’s no reason to be.