First of all, I think the folks whining about the 720p screen have absolutely lost their minds. If you go and actually look at the phone in stores, I just don't think that any actual human being can see anything "wrong" with the Alpha's screen. Compare it to anything in the store, and I doubt you'll find its text to be any less crisp than anything else. For crying out loud, you have to get out a magnifying glass with about 4x magnification to even begin to see that "awful pentile screen" break down into pixels. I think it's all utterly nothing but hogwash.
But, to answer your question, what Samsung would have lost with a 1080p screen is BATTERY LIFE. A 720p screen has less than half as many pixels as a 1080p screen -- about 44% as many pixels, to be specific. Usually, the screen uses the most power in any phone, and "more pixels" require "more power" to display any given image. And thus, the constant need for more power to display more pixels would substantially reduce the phone's battery life -- it's as simple as that.
I think it's a fine compromise that helped Samsung make the phone so thin and light, with its correspondingly smaller battery. If you really, truly need more resolution, then you probably would want a bigger screen to "show multimedia" and that kind of thing, and bigger-screen phones have plenty of room for bigger batteries, so that's the ticket if that's what you want. So, I sure don't see the Alpha as your best bet for a monster multimedia device, but there's certainly a market for smaller, lightweight phones, which the Alpha serves very well.