I have my own thoughts on this (I'm a teacher and a mum).
Unbeknownst to me for many years, a grade skip was a suggestion for me in primary school. The offer was to skip year 5. My parents just said no way. Very good call, as socially I would have hated it. When I was at school, age groups went from January to December. My birthday is at the end of July so I certainly wasn't an older one in my year level. Mum and Dad didn't tell me about it until I was as adult! I'm glad really, I was an anxious kid who didn't need anything extra in my brain space, and they were also very humble people who didn't want me getting a big head haha. I don't think I'm gifted. I think my Dad was though.
So when I was teaching year 2, a new kid came to the school and went into year 1. He was age appropriate for year 1 but one of the eldest. The teacher was convinced he was gifted and pushed and pushed for a grade skip. He ended up in my class. Great kid, I loved teaching him, but honestly, he wasn't the brightest in my class by any stretch. I don't think he was gifted either. I thought it was a mistake and told the principal on many occasions. That was the last grade skip in the school!
From a mum point of view, I see grade skipping as an absolute last resort. When I went to school, extension programs were virtually non-existent. Many schools now have so much depth and breadth in how the kids are taught that moving up is kind of irrelevant in my opinion. Our DS is in 3 extension programs in year 4 currently - literacy, numeracy and inquiry. He is thriving and when I see the incredible breadth of his learning experiences (compared to mine) I am quite amazed. Certainly at his school a grade skip would be unnecessary.