The problem with a tiered system in American sports is that nobody wants to pay top dollar for second-, third-, or fourth-tier games. Fans won't pay the ticket prices and won't buy the merchandise at the same prices, and television revenue wouldn't be in the same ballpark.
Vastly lower revenue would mean less money for the lower-tier teams to spend. They couldn't attract the top talent, so basically you'd have the English Premier league: a handful of teams that are competitive, and a bunch of also-rans.
It would downgrade the quality of play league-wide significantly, and it would bankrupt 2/3rds of the league. Not a great idea, in my mind.
The list of NBA champions over the past twenty years isn't too much more diverse than the lists of European champions. They have their Arsenals, Chelseas, and Manchester Uniteds, we have our Bulls, Lakers, and Spurs.
Top, rich teams have dry spells over in Europe, but they don't go under. I don't think it would happen with top teams like the Boston Celtics and NY Knicks over here, even if they struggled for a while.
We like to pretend that we have parity over here. We don't have any more parity. We just like to pretend we do. I say take out the pretense, and let those teams that don't have much of a realistic shot have something to compete for.
I would also add a tournament that's separate from the regular season championship like they have in European leagues. That way the second and third division teams would get their chance to play against the top teams. They might even pull some upsets along the way.
Another thing that would be crucial to the success of this league would be a development league team for each of the 30 teams where you could call up from or assign players to like they do in baseball.