As far as not being competitive, we have definite experience: Our 5 children were homeschooled. The last 16 of the 21 years were in Maryland. All 5 competed on swim teams. One was in the Jr. Olympics 5 times shooting Air Pistol (the first female State Jr. Champion for Maryland,) one twice, and one once. Three have competed nationally in BB gun. The youngest (age 15 and still homeschooled) recently returned from the BB gun nationals. Her team represented the state of Maryland. All 5 of the team members were homeschooled girls. The alternate was a public schooled boy. The team won 3rd of 39 teams, the best in the country. They joked that they would make a shirt for the boy saying, "we let him on the team because he shoots like a girl."
They all know how to cooperate, having delivered newspapers for 18 years as a team. They also know how to compete in a friendly way. They have friends old and young, male and female, Protestant, Catholic and part Muslim. One is married, two are getting masters degrees, one is in college, and one in the military overseas. The youngest is still homeschooled.
It is good or bad as the family is willing to work at it. Those who are not willing to put in the time and effort are better off with public or private schools. Those who are can get great results.
That's a neat story, and I hope you tell it wide and far.