The production costs for the first Shenmue game were in the neighborhood of 50 million dollars, which made it the most expensive video game at the time. A worthy sequel would take a lot of money to get made. I'd rather the series stay buried than be botched. Let's all be thankful that cheap Shenmue MMO cash-in never saw the light of day.
Well, the cost of the original ShenMue was huge because there were a number of R&D efforts going into it. There were no middleware engines at that time, everything had to be created from scratch (remember that development started on the Saturn, not the Dreamcast) so I would not take the first figure as a reliable benchmark for a production of this magnitude in 2010s. There are many complex games being made those days with much lower budgets (rather in the 10-20 millions range), a testament to productivity increase over time. 3D asset creation has gone a long way since 1997-1998.
I doubt a Kickstarter effort would be a silver bullet to get the game funded in its entirety, but it could well be a good place to start from and then have other partners (publishers or other investors) jump in to help fund the rest later on while work goes on.
I believe the goal of such a crowdsourcing effort for ShenMue 3 would also be to assess the market size for such a sequel. Honestly, no big publisher is going to bet on ShenMue and pour money in it. They are too risk-adverse. If it were the happen, the community, the fans would have to lead the way.