I'd posit that the way "miniature PC's" have developed IS primarily as a "communication, media, and information appliance". I'm pretty sure most PC users are Facebook users, Google browsers, website readers. I've no doubt that Apple (and Google) know this.
Fair enough. Netbooks are certainly the future of 'conventional computing', but running a desktop OS on them is probably not. Most people don't need a general-purpose personal computer, and keep buying them out of habit instead of need. I'm arguing, though, that consumers have shown quite clearly that they prefer the unified repository-style of media/software purchase and operation (Steam, XBL, ITMS, App Store, Android Market. All successes), and that seems to be the demarcation point between PCs and 'appliances' these days.
I don't see the link between that and access to Flash though. Surely an Apple or Google/Android smartphone user can still do those tasks regardless of the existence of Flash?
They can, assuming it doesn't cause ancillary problems, but it presents four possibilities. Either it works well or it doesn't. Beta quality software, quite usually, does not work well. Some don't like this release, some do. But it will eventually be mature, and by then we can reasonably and logically assess whether it provides a good quality of service over the wide variety of devices it runs on. Now, independent of the operation is whether or not it achieves its goals. Adobe would like Flash on smartphones to be what Flash for desktops is (or used to be):
the method to deploy video and rich applications. It either will, or it won't. If it does, then it reduces the usefulness of the Android Market and provides an incentive for media providers not to write native applications for Android. This is not good for Android, Google, or in the long term its users. Flash on Android isn't going to be as fast or flexible as native Android programming. So content providers and developers may not utilize user hardware to its best capabilities, and users will have no incentive to have platform loyalty. This, if I recall correctly, was one of Apple's objections to Adobe's development interface for iOS.
(and advertising, but both Google and Apple have their own ad distribution model for that).
Adobe doesn't get paid every time someone buys a flash ad, so it's kind of different. But you're right in that a good portion of flash utilization is for advertising, and this is another reason Apple doesn't have an interest in pushing Flash onto their platform. With iAds, they claim that their goal is to create a smoother integration of advertising into applications (for now, media later perhaps?), so that the application experience is not damaged and the advertisers can have richer content. Flash goes against that in their eyes: web advertisement is going to be different, they think, in a few years, because the way we use the web will be different.
I fully agree that Apple have their own infrastructure which they want to use for distribution of apps, and it's obviously in their own interests to not promote a rival technology! I think you've reduced the argument to the essence right there - but on here as well as other iOS fansites the reason will be because Flash "sucks"....

.
Don't expect sense from a rabble under any flag

.
Basically, Apple would like to reinvent the world wide web. They want to turn it into an "app". It'll provide a really rich experience for those who have the right hardware to access it. Those using it will never know what else is out there and be supremely happy. I hope it happens. It'll be the best of both worlds.
Ding! What a lot of people fail to realize is that
every platform benefits from a situation where rich content is by and large served on platform-specific implementations, but the web at large is standardized and looks the same everywhere, on every device. It prevents one platform's limitations from damaging superior platforms, whichever those may be at the time. It also promotes marketplaces which have the potential to be more secure from IP theft, which could result in more content and applications being delivered to more platforms and devices with less hassle and expense.