Nice idea in theory... putting it to practice might be difficult.
Take Baseball for example... where would you find a high functioning team from which you would pluck these players?
95% of the minor league teams are made up of players already contracted to a major league team. The independent teams are way down the ladder... Single A at best.
The players on the college teams are subject to the MLB draft, so the "stars" on this team will be split and go to the teams that drafted them.
Get brand new players straight from college then. The key is that ALL the team players know what the deal is. They all play as a team, not as superstars. And they're treated as such. It would be best if there were no players with any prior professional experience. Start with a clean slate. But I know that isn't possible in the professional ranks today. It is, after all, a business.