During the week of April 8th, Animal Kingdom opens earlier than any other park besides the Magic Kingdom. For the benefit and enjoyment of the guests who wish to ride such a popular new attraction such as Expedition: Everest, TWDC is spending hoards of money in overtime costs for exhausted cast members to open the parks for more hours than it has ever been open before. Disney is literally bending over backwards so the guests can enjoy themselves, and someone will always find something to complain about. Congrats, you are that someone, and not being able to ride one ride on opening day so you can impress your friends by telling them about your accomplishment is that complaint.
There is no timing issue, why do you know that Everest opens April 7th? Is it because of the internet? Is it because of the countdown pins? To a majority of the guests, the ones that go to Walt Disney World to enjoy themselves, to have a magical experience, they will not miss a beat. Its the internet that is ruining the attitudes of once fine Disney guests. That which you read about on the internet you become obsessed about, and the Everest Grand Opening is one of those things that a select few people are going to complain about, not because they deserve to ride it on a press event day, but because somebody told them that they can't, and that's what enflames the passions.
And about Iger shutting down rides to himself, he sure can, and if he does, more power to him, but he'll have to explain himself to the stockholders and board of directors... Similar situation, if he didn't have a grand opening event for the media after building $100 million+ attraction, he would have to explain himself to those same people.
As to why are they closing entire areas of the parks? I can only guess at two reasons, first of all, there are going to be a lot of media there, each with their own equipment, which requires a lot of room. Also, look at it from your perspective, maybe they are anticipating you, angry, with a false sense of entitlement, trying to get close to Expedition:Everest. Even shouting a few things, ruining media shots. Consider it a precaution to avoid having to escort those types of guests out of the park.