Things are not so black and white. To begin with, obviously Federer's style allows him to shorter points, but everyone here watch tennis enough to know that his defense is one of the most underrated abilities in men's tennis, specially in his prime. The guy ran like a rabbit you can see loads of those points in youtube, not to mention any full match from those days. Even today his defense is still quite good, and most fellow players when praising his sills always mention his movement. Point is, he indeed ran a lot, probably if, right now, we could sum all the "distance run" in all matches of all tennis players in history, if I would bet in someone to be leading this category, it would be Federer. He has the miles, no doubt about that.
So, on one hand I agree with Moxie, as there is always some luck in not getting injured. However, in a span of 15 and 20 years, "luck" is overrun by statistics, even if it will always be present at some extent. Of course, if you include "good genes" (short expression for a complex idea, but you all know what I am talking about), in the "lucky" department, then for sure Federer is lucky. He is also "lucky" to have all that talent...
Having said that, the main point for me is the mechanics of the movement. The greatest difference between Federer and Nadal, for me, its in this aspect, and is not even close. Yes, Federer spend, on average, less time on court, but I bet that if you make a full career comparison, the average difference is smaller than our selective memory tells us. But, even if we settle on a 20 to 25% difference in favor of Federer (and, considering the more years Federer have, the absolute value is similar), in no way this is comparable to the night and day difference their playing style have.
All Nadal's shots are "harder" to make. His effort to hit a single ball is considerably higher than Federer's, and that is all due to the way they chose to play. Nadal's forehand is built around the top spin, while Federer is built around his wrist and a fully stretched arm. Their backhands are obviously different. Nadal uses much more the body upward movement (to help the top spin), while Federer only "jumps" when he wants to hit it in a downward direction. Federer is much more keen to hit a higher ball without bending the knees, while Nadal will ALWAYS bend the knees and jump to get to it. Nadal moves his whole body to volley (it is always a bit strange to watch, but he does it quite effectively anyway), while Federer only moves his arm. The serve is obviously different and most things above in one way or another show up in the serve, even if Federer also jumps a lot to serve.
Anyway I am not advocating for Federer's style, just highlighting what for me is obvious. If you look this way, it is quite obvious why one style ended up with 10 RG's and other with 8 Wimbs... (which is the most stark difference of their careers). Given that their mechanics is so different, different outcomes are natural... so in this sense I agree that Nadal injuries are a "consequence" of his playing style (and would never use the world "fault" here).
What I don't agree is that he "should" change because of it. This is the most glaring and screaming nonsense I can think of. This whole package that people are asking to change (most times his own fans) is precisely the one that brought him 16 majors. 16! And he is still on the game for more. He kind of invented his playing style and thank the tennis gods he did. I agree that it "costs" more, but that is not a "moral failure" (to use Moxie's term), but rather a big, worthy virtue.