For the same reasons that every other government get-togethers and talks are accessible to the media. Public interest and trust.
Even the Obama administration has closed door meetings on policy issues. And what about the "classified" documents that Obama and his government generates? Public doesn't have access to that.
Why have royalty at these meetings?
They are all sitting on fabulous amounts of money and can act as market makers when they want.
Why media moguls but not reporters?
Like who? Katie Couric? You know what kind of dumbass questions the average reporter asks? What value would they add? Remember, I asked you to see from the perspective of someone on the "inside."
Why government representatives that are not in ruling government? (shadow ministers etc)
Cameron was part of the shadow government in the UK two months ago. Parties in power can change rapidly, so there is a desire to ensure continuity when the why-wasn't-it-fixed-yesterday ficklness of public opinion rears its head.
Such a meeting is elitist. Elitism is bad for the masses.
Why? You wouldn't make the same critique for groups of high level medical professionals in closed door meetings concerning best practices, why complain about it for finance? A bit inconsistent, no?
Its tyranny wrapped in cunning rather than muscle.
FWIW, most of the folks at that meeting keep us in line by force as a last resort. They do run the police and military forces of the world. In any case, nature is about domination, strength, and fitness. Look at how everything outside of humanity acts. We are not above nature, as much as you wish you were. Those who lack the strength or resources are subjects, those who have the strength are leaders. Nature.