The punishments were most definitely excessive in some institutions.
There is too much extant material to doubt this.
From my perspective, such punishment was cruel and brutal.
It is self-evident to me!
It may not have been if I had, in fact, lived in that era.
Winston Churchill suffered the most disgustingly horrendous birchings at his prep school but did not inform his family of them.
He was ashamed of himself and thought that his Mother and Nurse would be angry with him.
In his innocence, he believed that this was the way naughty boys were punished at school, and had no experience, no benchmark to judge, so he simply accepted them.
Perhaps other little boys who suffered were similar.