Your theory that players vying for the #1 spot won't play Davis Cup breaks down. Nadal has been playing Davis Cup for his country, he was even closer to #1 last year. Andy Roddick played Davis Cup while he was #1. Your example of Djokovic is interesting, but he has made it widely known one of his major goals is to win the Davis Cup, and that having a team comprised of all his tennis-playing siblings.
I think maybe you just fail to see the pride with which many (a great deal) players play for their country. Many players put their bodies on the line to play 5 set matches for their countries.
The idea you have to set aside a 3 week period would change nothing. In fact, you would see a lot of people who would use it as a 3-week vacation, just as many as use the Davis Cup weeks as vacations now.
What Tennis has is a unique team competition that allows anticipation to build up for an intense weekend of usually incredible tennis. You may say that you don't really get worked up for it, but other people do. Just because you do not does not mean that the tournament is a failure. In contradiction, attendance at Davis Cup event is really starting to rise recently as more and more people find out how thrilling these matches actually are.
You need only have watched some of the recent US matches which are televised to see just how thrilling they are. The US match against Chile was an incredible psychological battle, and Roddicks epic final set earlier in the year was awesome, even though he lost.
Maybe Nadal did feign his injury and is a little more interested in the clay-court season, based on what I've read about him I doubt, but maybe. Let's say I give you that. Okay, now the top 2 players are sitting out of Davis Cup because they are solely focused on themselves. Now explain to me why there are 1500 other professional players who would gladly play for their country and how that fits in with your theory. And after doing that, explain to me just exactly what is so wrong with the competition that so many people would want to play it, even if they don't once they get up to #2.