I have the feeling that Flash-based ( or Silverlight-based) websites are generally frowned upon, except when you are creating games or multimedia-content rich applications.
In its defence, most of the issues raised here about how people have implemented Flash in their websites, not about Flash itself. Flash does support accessibility it's just that most people don't consider it when building their sites. Flash does work on mobile phones - it's Flash Lite, although the ActionScript is limited in earlier versions.
Why should anyone have an automatic right to view the source code of a website? A web author has spent time and effort dreaming up their code to share their ideas through the medium of the web. If you want to know how something works, why not put a bit of effort in yourself, and work it out? The beauty of the web is the message, not the medium.
So what if Flash is owned by a single company - Adobe bought it for a reason, and that's because it's a fantastic bit of kit. The problem comes from web authors not using it properly, trying to make it do things it was never intended to, or simply not applying standards to their sites when developing using Flash.
What is so evil about a Flash based website? Absolutely nothing. It's like asking what is so evil about a gun. Nothing. It's the idiot wielding it that has the problem.