It really wasn't about peaking too soon. Ultimately, you can't expect to win a championship when your 2 best players are 23 years old and only have 3 years of prior experience to draw on.
Magic, Bird, and Duncan are the only young champions to lead their teams to the title but they were on teams stacked with veterans who had been in the league many years and some of them had either won championships or played in NBA finals prior to their arrival. And they were Magic, Bird, and Duncan - 3 of the smartest basketball players to ever play the game. Everyone else, superstar player or not, had to learn how to win the hard way... by losing.
Dr. J lost to the Celtics, Blazers and Lakers in the Finals and didn't break through until the Sixers got Moses Malone.
Zeke lost to the Celtics multiple times and then lost a heartbreaking series to the Lakers in the '88 Finals.
MJ lost to the Pistons multiple times.
Drexler lost to the Lakers, Pistons, and Bulls. He finally won near the end of his career after being traded to Houston to team up with Hakeem.
LeBron lost to the Celtics multiple times and then lost to the Spurs and Mavs in the Finals before capturing his first championship in year #9.
Many of the teams that the above players were on had great regular season success. Several of those teams had better rosters than the Pacers had this past season. Yet, they still lost to teams that were either more talented or had more experience. So it wasn't really fatigue or peaking too soon that did the Pacers in. It was youth and immaturity.