So why does Amazon get to set the price, and not Apple or the publishers?
Because that's how the sale of every other product to the consumer works - the manufacturer or publisher tells the retailer "we'll sell you a crate of widgets for X dollars apiece" and the retailer is free to sell them to the consumer for whatever they think the consumer is willing to pay. Usually it's some function of X, but it doesn't have to be.
Agency pricing (so-called because the publisher sets the retail price and the retailer acts as an agent of the publisher, taking a fixed percentage of that as his profit) removes the ability of retailers to compete on price. Apple liked it because they don't want to compete on price anyway. It doesn't matter so much when you're talking about their hardware - plenty of people are willing to pay a premium for an Apple computer or phone or tablet because they perceive them as better or cooler than cheaper products with similar specs from other manufacturers. But if you're talking about ebooks, it's hard to see why you should pay $12.99 or $14.99 for the latest Stephen King or James Patterson from Apple when you could get exactly the same thing for $9.99 or less from Amazon. But if it's the same price at Amazon, you might as well get it from Apple.
The publishers liked agency pricing because it meant Amazon couldn't price ebooks at a point where it would cut into the publishers' print business. The publishers know that print is going away anyway - they're just trying to prolong it as much as they can because they know that when Barnes & Noble goes bust, there won't be anyone else they can play off against Amazon. They also know that print distribution is the last advantage they have over self-publishing. Self-published ebooks now compete on a level playing field with ebooks from the big publishers, but it's still very difficult for a self-published book to sell a lot of copies in print. (The ones that have managed it were usually picked up by a publisher after doing well as ebooks.) Everything else a publisher can offer an author can be bought from freelancers for a one-off fee, instead of most of the revenue for the life of the copyright.
Having said all that, the lawsuit was never about agency pricing as such. US competition law cares very little about protecting retailers. What was illegal was that Apple and the publishers colluded to raise prices, thus harming consumers. The fact that they used an unusual method of pricing to do it is neither here nor there, really.