From my own experience as an app developer, selling the same app on the Mac App Store and through my own FastSpring based store, the Mac App Store is fantastically more profitable. We have a free trial which offers a seamless in-app purchase through our FastSpring store, and we also offer bulk purchases and enterprise discounts through that store, yet the vast majority of our sales are through the Mac App Store. From my numbers, only one day have we seen more copies sold through our own store, and the revenue that day was still less than the Mac App Store's.
From my own experience as an app purchaser, the App Stores rock. I can quickly download and install any and all purchased apps on any and all of my devices. I don't have to worry about serial numbers or registration files. I don't have to worry about nefarious acts that might compromise my download. Hell, I don't even have to worry about installing. The app just appears on my system, ready to go with a single click.
So, from both sides of the field, Apple's App Stores offer a fantastic experience. Are there downsides? Sure. As a developer, I need to worry about bugs like the OP hit and I need to deal with Apple's approval process. But that said, I have to worry about bugs in my own store and purchase validation code (bugs happen there, trust me!), and the approval process leads to the huge upside I and everyone else experience as consumers. And if that process makes consumers more willing to purchase my product, I'm willing to pay that price.
You can call the ecosystem "closed" and you may feel Apple doesn't "care about their developers" but, from my point of view, Apple's provided us with a fantastic platform, some of the best dev tools out there, and the single best software storefront that exists today. Personally, I'm feeling quite cared for and don't see any other platform or storefront offering the same experience. Not by a mile.
Apple has been treating their developers like crap ever since the app store opened, and the only way to change it is to vote with your wallet (or more accurately in this case, your development time). Otherwise, you are part of the problem.
How does it work? Do you just send ipa files that the user is expected to import into itunes?
People already complain about too much competition on the App store. On the web you're competing with virus' and everything else as well. And people have to figure out where you are.
Having your app on the App store is like having it in some giant big box store. Having it on the web is like having your app somewhere on the planet.
For iOS apps: Most of the time you don't. You could write your app as a mobile web app, but that doesn't cut it for a lot of apps. If you're determined to have a legit iOS app, you're playing Apple's game.
For Android apps: You can distribute on a number of app stores, in addition to or instead of the official Android Market. You can also offer downloads that can be installed manually, although this requires users to change a setting to allow so-called "sideloading" of apps.
Jailbreaking is simple and performed by millions. Support issues aside, if I were selling iOS software I would offer it in the App Store as well as on Cydia.
That said, yes there are alternative app stores available for iOS devices but I would hardly call them "legitimate" since Apple defines that term with respect to their devices. The sad truth is that you have to bypass Apple's restrictions, and continue to do so for each new iOS release, to benefit from an alternate app store like Cydia.