In case it's helpful to hear from someone who was accelerated, here's my $0.02.
I skipped first, about 40 yrs ago, then moved and spent the rest of my years in a district that didn't do acceleration at all (though they didn't move me down a year); while I could've used the challenge of further acceleration, it wasn't an option, so I can only speak to a one-year skip.
I would say it was the best option for me *under the circumstances*, but still deeply suboptimal. It was the better of two bad options. (The best, but not at all available where I lived, would have been to be grouped with a cohort of intellectual and age peers in a gifted-ed setting.)
School was easy, even with skipping. I could pretty much coast and get As. It was better than being in my age-cohort class would've been, but still not a challenge. I still lack good study habits.
Being a year young and in the wrong setting (only ~10% of my class went on to 4yr college) definitely harmed my social and emotional development.
I'm tall, so I didn't stick out in that respect, but I believed I was bad at sports (nope, just a year younger than everyone), not cool (nope, turns out I was once I got to college), and had no social skills (nope - again, just a year younger than everyone and didn't really have any shared interests; turns out, I had plenty of friends once I got to college).
I'm now a successful professional but I still can't shake those negative self-perceptions and self-doubts, even with a college varsity letter and plenty of experiences showing objectively that I'm *not* awkward and I *can* make friends.
I finally found my people when I got to college, and it was AMAZING. I've always envied the people who had intellectual peers the whole way through.
TL; DR: I can't say you should always or never skip, because it really depends on the circumstances. If possible, get your child in a setting where they have intellectual peers who are also age peers.
