One thing that really bothered me during my PhD is that even at the Stanford math department it felt like academia is not set up to encourage work on big questions, nor is it optimal for any objective function I can think of. Is it any wonder that many of the recent breakthroughs (Perelman with Poincare, Zhang with prime gaps) came not from establishment mathematicians, but ones who couldn't or wouldn't play the academia game and ended up almost destitute on the fringes, working away at these problems that they knew inside could be resolved.
Now, why specifically is the Riemann Hypothesis a great place to start? Math problems are like a maze. There are many paths to take, and while you can take satisfaction in exploring one part, you won't know your progress until you see the exit in front of you. In the case of RH the branch factor is absolutely massive, but once you pick a direction, it doesn't take long (relatively) to get to the forefront of what's known. But as it stands it is very hard to get perspective on the problem, or know which ways are good or bad. A mathematician who is not an expert in the field may experiment with various ways of bounding Zeta away from zero, but a domain expert would right away point out positive vertical density results for all a-sets, and bounds on moments of 1/zeta(s). Worse: if you have an idea for a new approach, there's no good way to share it because it will likely be too small for the quantum of academia: the academic paper. Building a collaborative atlas for the Riemann Hypothesis would help solve both of these problems, and could provide a more structured way of working on hard problem than even the polymath projects. It'll be a challenging use-case but at least with 150 years' of work there will be no cold start problem. And I've seen many analytic number theorists who are incredibly smart, hard-working, insightful, great with programming, happy to get their hands dirty, eager to teach others, but neglected by the system and lacking an outlet for their skills. PS: There's still no clear reason to believe RH to be true rather than false.