It seems to me that they could easily introduce the 9.7" iPad 2 with a higher resolution, as has been rumored, AND a 7" iPad that has the SAME resolution (1024x768) as the original iPad, no?

Problem solved.

Sure, apps designed specifically for the original iPad at its original resolution will have UI elements that are proportionally smaller, but I don't think that would be enough to kill usability on most apps.
As for the people who say typing on a 7" iPad would be too tough... um, iPhone?

I type pretty quickly with two hands on my iPhone 4 in portrait mode no less, though I admit one-handed typing on my iPhone is tough given my big man-hands.
If Apple does sell a 7" iPad, I would likely get THAT instead of the larger iPad, due to the increased portability. I want an iPad I carry with me basically everywhere that is somewhat pocketable at least, as I have seen with the Samsung Galaxy Tab. This is particularly of interest to me as I am migrating away from iOS for my phone (have had a 3GS and 4 now) as I am moving to Blackberry for my phone usage; however, I still love the UI, browser, and the richness of the apps of the iOS platform, and would love an iPad of the 7" form factor to carry when I want a larger screen than my smartphone.