It still takes a long time for the initial page to load. We don't even get a loading bar, just a blank page and "Built with Hype" for seven seconds. When it does load, we still have to sit through all the pieces of the page sliding into place. The demos look like Flash pages straight from the 90s. And I dare suggest that Flash sites could be more SEO friendly.
Hype seems like all the annoyances of Flash under a different name. It seems to encourage bad, flashy design just as Flash did, which makes me wonder about your "[t]his is a very designer-friendly process" quote.
Inability to recognize and use the operating system font preferences like hinting, resulting in AIR apps looking ass-ugly on some systems.
Tendency to grab focus and have its own dumb hotkeys that don't match (or overlap) common/native conventions of the platform.
Its own set of security vulnerabilities and its secondary tier of cookies which browsers have no control over.
Flash not only has issues with "mobile devices", it severely hurts everyone who's trying to create new platforms - any kind of platforms. If you want to tinker with a CPU and a pair of micro-controllers, after some soldiering and bootstrapping linux on it you'll be able to run any web app you want on your very own platform, which is cool. Flash prevents this from happening in the first place.
The last paragraph is by far the #1 reason why Flash should not exist. I wish Mozilla and Google would simply drop NS extensions support one day, and the plague will be gone the day after.
What exactly does this have to do with flash though?
How does flash really prevent you from doing this? I suppose you mean without a flash-player on a platform you can't run swf's? Well okay, I think "prevents" is the wrong word here, even though I don't just mean to nitpick.
The biggest selling points for flash are it's ubiquity and the fact that you get around the download-hurdle when using it. It will be a while until there is a solution that 1) addresses those two problems and 2) does everything that flash does and does it just as well.
Of course flash isn't perfect, but there are good reasons for why it exists and will remain doing so for at least the near future.
Seems like you answered your own question. Those are two major problems with Flash.