The management is the same. DCL is actually run out of Celebration Place by Karl Holz, who came up in the Disney ranks at WDW from 1995-2002 and then ran Euro Disney before being moved over.
I think the answer is complex, but they believe they have a blue ocean product to begin with. They are unique at sea in many areas (from having lavish entertainment -- something others are catching up on -- to no casino to fireworks etc).
Also, they are able to command HUGE and I do mean HUGE premiums over the competition. Cruising can be a very inexpensive vacation, but not on Disney (with a few exceptions that I generally take advantage of). I see folks spending more on 4-night Dream cruises to the Bahamas than I have spent on 9... 11 ... 14 night cruises with other lines (and in some cases with DCL). When you are charging so much more than other lines, well, you better deliver a top notch product.
It's the opposite of WDW where they keep raising the prices and now ... well, they barely have a market for their deluxe resorts so they DVC them all and keep raising prices at all tiers. The idea that the rooms at the value motels are now well over $100 much of the time and over $200 at the moderate motels is just evidence of this model. They can still put rubes into the lower category rooms at absurd premiums. But getting those folks to pay $900 for a parking lot view room at the Poly for Christmas just ain't happening.
They wrongly believe they can keep raising the price points in o-town with no pushback. If they actually studied their business and the market, then they'd know they've already long past the tipping point.