Flash is pretty slow on a Motorola Milestone with a 550MHz processor, but it's fine on the current crop of 1GHz smartphones, and the dual-core Motorola XOOM tablet.
The iPad 2 could easily run Flash, and so will the iPhone 5 (and, I'm pretty certain the iPhone 4 and iPod touch 4G would not suffer).
It isn't a simple case of whether Flash can run.. this is a 'political' issue and Apple is doing pretty well, especially having successfully convinced many people that Flash is evil.
While Flash IS evil if designers don't use it properly (like building websites exclusively in Flash) or run on some really underpowered netbook with no RAM, it isn't an issue on modern hardware that exceeds the needs of most people and is rarely pushed to the limits.
Mobile phones and tablets will only continue to get more and more powerful as manufacturers play the games of the PC industry. Just as we have cameras with squillions of pixels, we now have people buying the fastest smartphones. Will many of them need that power (it won't make the UI any quicker!)? Who cares. It's something to impress your peers with.