(I can only offer anecdotal commentary.)
It really depends on the child. I was starting to read and do addition/subtraction at age 3. I wasn't pushed, but as my parents realized my potential, they supported and encouraged me. That support evolved into home schooling.
I did go to public preschool and kindergarten (half day sessions, home schooled the other half). There, the teachers accepted my ability and appreciated my willingness to read stories to and help the other kids.
After that, even though the school's officials acknowledged I was performing at a 3rd grade level, they insisted that I had to be placed according to my age. Being 6, that meant 1st grade. The teacher quickly determined that I always had all the correct answers, so stopped calling on me - not even calling me last, after the other kids gave up. And while I was allowed to participate in group "reading aloud", he was irritated by the fact that I had finished reading whatever story before the other kids were even ready to start the reading session. Also, I was not allowed to help my classmates. While he could not mark down my workbook, quiz and homework scores, he did give me zeros for class participation and "citizenship". When my parents complained, the teacher demanded the school officials assign me to a different teacher. After a week of only slightly better treatment by the other teacher, my parents decided to pull me out and resume home schooling me.
3 years later, a new private school opened. My parents arranged an interview for me. Near the end of the interview, the teacher looked at the public school records and commented "I'm sorry about what the public school did to you. But don't worry, you're the kind of overachieving trouble-maker we want," making my parents laugh. She excused herself, then returned a few minutes later, telling my parents that no further review was necessary and I would be accepted on full scholarship.
I think I got the best of both worlds. Home schooling provided the academic challenge I needed (and wanted). Preschool, kindergarten, Cub Scouts and other activites provided the social development opportunities. Then the private school continued both.
While a bit of strife may help build character, being held back academically is a lot more than a bit of strife. Being home schooled was not easy. My parents gave me lots of challenges, allowed me to meet those challenges, then setting new ones.
Do your kids a favor. Help them set achievable goals. Provide guidance (not easy answers). And don't be afraid to say "I don't know. Let's learn together."