I have been reading more or less all of my books for the last year on an iPhone. The screen is a bit small, but it's made up for the fact that I can take all the books that I want on international trips and not have to pack anything more than the iPhone that I was going to be bringing anyway. I have the font upsized quite a bit so there's not a lot of words to the page, but I have read about 15 or so books on it without a problem.
As far as eyestrain, I spent my entire day reading off of a backlit display (the LCD screen on my monitor)... I agree that e-ink looks better and is a huge improvement over a backlit display for reading in bright sunlight, but I would bet the primary advantage of e-ink for an e-book is not the picture quality, but the fact that it only uses power when it changes the screen image and thus you can achieve a battery life of weeks compared with a battery life of hours with an LCD. I know what eyestrain headaches are like and I've never gotten one from reading on an iPhone. On the other hand, I won't buy an e-ink display because one of the big advantages of a backlit display for an e-book reader is that I can read in the dark when my wife goes to bed and read in comfort in low-light conditions - like a night flight on an airplane.
My only complaint with an iPhone as an e-book reader is the size of the screen, and the resolution of the screen. I'd like a higher resolution, larger screen.