No doubt, it is a step NOT to be taken lightly.
Rarely happens in the rural area where I live and coach now. In more suburban areas where there are a lot of private day schools, it is more common, especially for athletes.
If done later in HS, and if done haphazardly, it can have potentially negative consequences if not done for a seemingly legitimate reason (makeup year for a year lost due to injury or other reason, shoring up academics for HA recruiting, shoring up skill set, etc) it can appear to be an act of desperation and likely a turnoff for coaches recruiting; especially if the kid is still the same kid they saw the previous year and closed the book on.
Former travel ball player of mine was a very gifted baseball and basketball player age 12-14. He graduated 8th grade middle school and dad enrolled him in the local Catholic school for another year of 8th grade. Dad then sent boy to local HS for the next year of 9th grade. Then somehow managed to get him transferred to crosstown public HS for 10th grade, and yes, 4 years and 4 different schools. A bit much for my taste, but not my kid so more power to him.
In the end the young man is playing baseball in college. Worked out for him but I think he would have played college ball if he stayed true to his original grad year.