I think this whole "young guys need to earn their minutes" thing is way overstated, and more than a little parochial. Of course, I also don't think that you just toss young players to the wolves in the hopes that they'll become great through simple exposure. There's certainly a much happier medium to be struck that is neither condescending nor overindulgent.
For example, Gregg Popovich played Tony Parker nearly 30 minutes a game during his rookie season, and nearly 34 in his sophomore season. Those are some big time minutes for a player who was drafted 28th overall, and who few in the NBA thought would amount to anything. And Parker actually was quite erratic early in his career. If he overstepped the boundaries of Pop's gameplan, Pop would call a time out, pull him from the court, give him a fierce tongue lashing, then get him back into the game at the next whistle. He wasn't worried about whether or not Parker had "earned" his minutes. Instead, he made Parker's minutes count by carving out teachable moments from his mistakes. The same went for Manu Ginobili, who drove Pop crazy early in his career with his free-wheeling style of play. But Pop has always known that talent matters above all else, and you need to find ways to harness the talent on your roster, no matter how young or undisciplined. You mold the talent to become more disciplined with time, while preserving that which makes it valuable in the first place. If it can't be disciplined, you cut it loose.
All of that said, I don't think the Kings would be doing themselves any favors next season by gluing their young players to the bench--with all the subtlety of a schoolmarm--until they've "earned" their minutes. You need to see what you have in these guys. Figure out the hierarchy of your young talent, then get as many of them on the court for 30+ minutes a game as you can. And don't just let them struggle through those minutes. Pull them when they make mistakes, but with the knowledge that they will be returned to the court as soon as their error has been made clear to them. I don't like when the coaches of young teams yank their players for making mistakes and then withhold further minutes as an ill-considered kind of punishment. It doesn't teach them anything but to play with fear, and the last thing that any team with future playoff aspirations should want is a bunch of tentative young guys going through the motions and never truly developing (which might not be a bad description for the Kings teams of the last decade or so).