This was the traditional MBA path for a long time. Start out in a technical field (e.g. engineering), go back for an MBA, move to a management position. A lot of the value of the MBA comes from sharing previous experiences w/ your peers. Having students go straight from undergrad to MBA dilutes that value significantly and it doesn't really do the student taking that path any justice. They'll likely come out and hit the workforce more entitled than they normally would be.
A lot of things mentioned in this discussion deal with leadership issues. MBA programs understand this and focus more on it but leadership is a difficult thing to teach. There is still some hard skills gained in an MBA program, essentially being able to jump into a business in a consulting role and be able to function across multiple departments to understand the business.
In an alternate scenario: an MBA gets hired to fill a position below management and the higher-ups get a clear picture if they're cut out to manage operations, only awarding the MBA a promotion to management if/when they prove themselves.
To get in, you need great work experience, great recommenders, excellent test scores, and a great story. Basically things that signal you're generally pretty smart and can learn quickly.
Most people in MBA programs are there to either a) help jump their career into a higher bracket (i.e. management) at companies where having an MBA is one of HR's checkboxes or b) move into consulting.
So I wonder are the Elite programs significantly different than other programs?
One of my biggest problems encountering MBA students released into the wild is that so many have limited life experience. It's really hard to explain to a fresh MBA guy that you can't schedule people only when it is convenient for him / how to cultivate personal / professional relationships / how to just theorize customer's responses to various changes (like thinking beyond saving 1%) and etc. It's just so hard to teach folks who haven't the experience these things that being a good manager isn't just pulling the mechanical leavers of management because "i'm the boss" and how to really understand what leadership is when they haven't experienced it much from the other side.
I haven't encountered many from the best programs and I always wonder if they require some REAL work experience where they had real responsibility first / etc.