This is what Bettman would say, and it’s an effect of the cap (escrow is really where this comes in mostly, I’d say) but the real reason is and always will be parity.
Don’t want any teams to be too successful, or any teams to be too bad. That’s what has been growing the league, everyone seems to get a turn because good teams can’t stay too good for too long and bad teams can’t stay too bad for too long, because by being successful your players will get raises, forcing teams to distribute those players through out the rest of the league.
Redistribution of talent
Stop. The league doesn't care if TB is in the Final 4 years in a row, winning 2 or 3 times. Before players had an increased say in where they played, Edmonton of all places could have a dynasty. Montreal, the place nobody wants to go to because of taxes, could have a dynasty.
Talk about parity, back in the 80's, 76% of teams made the playoffs. Today that would be like the 24th overall team in the playoffs, every year. That was a choice the league made. The 2nd worst team in the league, in Toronto of all places, made the playoffs one year due to the, wait for it, playoff format. Back in 1967, when real men were in charge, they guaranteed a spot in the Final for 1 of 6 expansion teams. I don't care what you think about Vegas, they never got that road to travel. There was no guarantee. Not to mention, after that expansion draft, nobody looked at that roster and said contender. If anyone says they did, they're a liar who just hates anything Bettman.
If you're good and ruthless enough to win 10 Cups in a row today, Bettman ain't gonna care. The cap is about cost certainty, end of story.