The advantage with starting with breakfalls:
I haven't seen Ellis Amdur's DVDs, but this is pretty much how we start in Yoshinkan aikido kenshusei course. I had no previous aikido experience, but I was doing all the breakfalls in the syllabus within a few weeks.
I am at a little bit of a loss when I hear people talking about getting injured and having fear doing breakfalls. I am not a natural athlete, and I have balked at doing forward rolls over 4-foot barriers and over 3-4 people squatting on the ground. But basically breakfalls don't seem scary to me, and I haven't gotten injured.
One big difference (as I understand it) between Yoshinkan and Aikikai is that in Yoshinkan, the uke collaborates with the fall. The advice on this forum to resist throws seems really dangerous to me. You follow nage and throw yourself if the technique doesn't work. Otherwise, you run the risk of having the throws force locate in a place you don't want, like a joint that can't bend because it's locked out.
Even though Yoshinkan is a "hard" style of aikido, from what I have read on this forum, I would say Yoshinkan's style of teaching breakfalls is a lot better than other styles. And it's very simple. No big build-ups, just start doing it. Once you realize you aren't going to get injured, even from a hard fall, the fear goes away.
One thing I would mention is that the most thoughtful of our instructors avoids doing hard falls unless he has to. I do think that over time the constant battering will take a toll on the body.