In our district the only way that a child can be held back, with permission of the school. They involve the school psychologist, Teachers advisers and principals.
In my oldest sons third grade year, They wanted to hold him back and repeat the third grade. He had already been held back once, which I thought was justified. However I was against this second time. My oldest has severe ADHD. it effects him still today. If he was held back yet again it would have put him in the same class as his youngest brother. I believe that would have been harmful for both of them. My wife and I had no idea this was coming. We were called into a meeting, initiated by his teacher. After we heard that she was suggesting holding him back, we asked for a meeting with the principal. He brought in the school psychologist, after discussing our concerns, the psychologist talked to our son and to the teacher. She reviewed our sons EIP. She was very upset. The teacher had not been following his EIP, and had other reasons, she would not share to believe why the teacher wanted to hold our son back.
The Psychologist, suggested against holding him back and prescribed a teachers aid to assist and verify that his EIP was being followed. I would like to say he blossomed and did very well in school the rest of the way. Unfortunately school was always a struggle for him. However I believe if he was held back things would have been much worse for both my children.
If a child is well adjusted and doing well in school, our system will not allow the child to be held back once they have started school. In our area, parents delay sending there kid to kindergarten for a year. The Academics are well respected at our public HS. Few privates, which are mostly Catholic, hold transfers back a year.
So in many area's it is not always and easy thing to hold a child back. Many schools will want to help the child adjust, or provide assistance. If you truly believe it is beneficial, I would suggest that it be done before they start school. If my boys have sons, we will probably discuss this with them.