^ What Mittsie said. But to elaborate...
Many reasons why fans cannot and should not take it upon themselves to raise funds "for Shenmue 3" -
1) We don't know how much investment Sega would need in order to make the game. Only Sega knows.
2) Sega needs more than money to make the game. They need to be able to commit time and resources, which means taking staff away from other projects to work on this one. We don't know if or when Sega can make those rearrangements. Only Sega knows.
3) Why should the public trust an unofficial, unendorsed fundraiser to use their cash for the advertised purpose? With the best will in the world, there'll always be a suspicion that at least some of what's raised will be spent on hookers and crack.
4) If reason #3 results in people withholding their donations out of caution, it would misrepresent the demand that exists for this game. Sega would be given the false impression that people don't want the game after all, when in fact that isn't the reason they haven't paid up.
5) If the fundraiser fails to result in Shenmue III, for any of these reasons (and it only takes one), then people will be twice-shy about backing any legitimate, fully endorsed fundraiser that may happen down the line. They'll feel like they already tried this and it went nowhere, and so they'll pass up their chance to really make it happen.
6) Lastly, Kickstarter itself has guidelines stating that a project on the site must have "a clear goal, like making an album, a book, or a work of art. A project will eventually be completed, and something will be produced by it." Without Sega's prior approval, this cannot be guaranteed. The guidelines also state that examples of prohibited use include "promoting the donation of funds raised, or future profits, to a charity or cause." So a fan-organized Shenmue III fundraiser on Sega's unsolicited behalf would not even be allowed on Kickstarter.
In short, as exciting an idea as it may seem to "take the bull by the horns" and raise the money for Shenmue 3 ourselves, in practice it would not only be fruitless but would very probably do more harm to the game's prospects than good. It's a nice thought, but it should remain just that.