I won't rehash my own whole story here, but highlights from my own experience and the experiences of my siblings, with multiple grade skips/radical acceleration:
1. The social adjustment was easiest for females.
2. Having a strong, stable peer social community outside of the schooling environment moderated (did not eliminate) the social impact of multiple skips.
3. For at least one sibling, widening the social gap with additional skips was the least-worst alternative to intellectual asphyxiation. Asynchrony is going to be a factor one way or the other; minimizing academic mismatch was more important for these particular learners at those particular times. That's a conversation that needs to be had: which aspect of asynchrony is the least/most detrimental at this time.
4. It was vitally important, if not absolutely essential, to have informed consent from the child. One of us was offered a placement that would have resulted in full-time matriculation into college at 13, but declined it, on the basis of a thoughtful self-assessment of social-emotional maturity, entering the program a year later, instead. In retrospect, that was a wise joint decision between parents and child.
5. You can only make decisions based on the needs of the child in front of you right now. Available resources, and more importantly, the child's needs, can change very quickly. A skip (or no skip) now doesn't necessarily lock you into any particular path.