Anyone who says that Edge is not fast enough to handle Flash knows nothing about SWF. SWF is one of the most optimised file formats known to man. Go look up the specs and see how tightly vector graphics are packed - it's insane. Pretty much everything is packed bitwise, co-ordinates included, so all the opcodes required to draw a square total about eight bytes or so. (I've handcoded SWFs without using the commercial Flash authoring system, it's kind of fun. Usually i use Ming, the truly awesome open-source SWF-generation library.)
Video takes up bandwidth, sure. But there's a lot more to SWF than video.
A useful website that requires Flash? Here's one I've done: the online map editor for
www.openstreetmap.org (kind of like the Wikipedia of map data; you need to register to be able to use the editing function). About 2000 lines of open-source ActionScript. ActionScript's drawing API makes it a breeze to code and you're guaranteed it works the same on all systems.
As for "AJAX is a movement based on web standards" - well, maybe, but AJAX is also based on a feature (XMLHttpRequest) developed by Microsoft for Outlook Web Access. It's pretty cool, sure, but I don't think it's got many more "standards" brownie points than SWF - which is an open, published file format, albeit one where most future development is controlled by Adobe.
After all that, I would say: don't get your hopes up too high for Flash on iPhone. I mean, I really hope it comes and I hope Apple are developing it, but remember that Adobe still haven't managed to ship a 64-bit version of Flash Player... and porting it to ARM is a whole load more complex than that.