Yeah, it definitely happens... but that said, so does the opposite. I could make a pretty long list of early cup winners that won several cups through their careers. It's a hard trophy to win, so it would make sense that there'd be a lot of players that win early in their careers, and then never again...
Ville Nieminen as a fifth finnish SC-winner after his first NHL season. Kinda odd to see him there as previous winners we're consired like legends. He played only 6 seasons in NHL after that in different teams and another 4 in europe (currently in KHL) but i guess he can be happy what he achieved.
He won the Stanley Cup in his rookie season (led the league in goals and points as a 23 year old) and 15 seasons later retired with no more cups (two Hart trophies though and 13 seasons top-10 in NHL goal scoring).
Bobby Hull could be included with 1 Cup win in 1961. Although it was his 4th NHL Season he was only 22 when he won it. Mikita (top of Pnep's list) was on that team also (in his second year) and was just 21.