I have a few problems with your argument. The first is that the Raptors won't have $40 million in salaries. They'll have $45 million. And if the cap remains exactly the same, that means they'll have $13 million to spend, not $20 million. Of course, none of us have any idea WHAT the cap will be next year, and it very well could go down, depending on what the owners try and negotiate. And there are actually 8 other teams that will have either the same or less salary requirements this summer. Several of them have more talent on the roster, too.
As for the team needing veteran leadership, I disagree. It's nice to have, but if Oklahoma proved anything it's that you can allow your young players to grow together and don't need veterans to learn how to win. I do think it helps, but I don't necessarily think those veterans need to have prominent roles to help.
The Clippers are a very bad example because they have simply been mismanaged. It wasn't relying on the draft that has made them a perennial loser, it's simply bad drafting, bad trades and bad signings that have done that. Just take a look at their drafting record...
http://www.82games.com/bestdraftingteams.htm
The teams that end up in the lottery year after year are not there because they're trying to build through the draft. They're there because they're not well managed teams.
I also don't like the "tanking" suggestion. I'm not saying the team tanks, but I'm saying to continue to build with youth and not try and hurry up the process, which will likely lead to another lottery pick next year. That's not tanking.
The Chicago Bulls example doesn't work in your favour, because they already HAD a young All Star with the potential to become an elite player, as well as a potential All-Star, in Noah. The Raptors have none of that. Take away Rose and Noah, and add Boozer, and you've got a mediocre team that would struggle to make the playoffs. That would be the future of the Raptors. However much I like DeRozan, Davis and Amir, none of them are surefire All-Stars and I wouldn't be surprised if none of them ever are. You simply need more talent to start with if you want to try and make a run for the playoffs, unless simply making the playoffs is your ultimate goal.
A team definitely can go from mediocre to a contender very quickly, but you need the right pieces to be able to do that and the Raptors simply don't have those pieces yet. And they're not getting it in a trade involving Bargnani and the 5th pick.