Applications: (1) JIT service and product supply chains (2) redundant service and product supply chains (3) dynamic fiscal/product/service logistics (4) overthrow ridiculously endemic middle-men in B2C/B2B (Alibaba, Amazon, Ebay, Taobao, etc.) who provide poor reputation, settlement, escrow and search solutions (5) make sense of 1000s of available shipping and logistics providers (6) change-ready open source fintech supporting nontrivial (eg. multi-currency, multi-stage) risk/transaction/execution models (7) non-conventional asset/settlement-ready decision-making and BI solution (eg. social credits, environment schemes, etc.)
The plan: get generalist people with background in related disciplines together, churn out something usable on a 24x7x365 multi-jurisdictional basis by real businesses, make some functional examples, let it loose, claw some market share from the incumbent closed source players, possibly derive revenue from the subsequent growth in connected services (FX, warehousing and logistics, legals, multi-jurisdiction, e-government) or just fund them as separate entities.
Note that this meets the "stuff not being worked on by hackers, or that is un-fundable by others" suggested requirement, basically because its slightly too big-idea for individual hackers, and too cut-off-the-hand-that-funds-it for most businesses with stakes in the effected domains. It is also a little edgy for most governments, who would prefer people to default to a centralized fiat asset system that is more taxable but usually very high-friction and change resistant. It is also very connected to the basic income notion, as it should easily facilitate concrete modeling of the benefits of such against arbitrary academic models, including actor-emulation, risk-model tuning for all parties and failure simulations: Chaos Monkey for business, economic, legal and social systems. Quite possible impact in law.
It should also work well for modeling a lot of the other ideas presented in this thread and others (eg. Shypmate et al), so many in fact that quoting them in brief apparently exceeded a length limit.
The fact that so many of these suggestions could potentially benefit from a decently extensible, actor-based approach to economic (maybe 'social') and risk modeling becoming open source standardized (and thence easily neural network explorable) suggests strongly that it is a useful area of research. When the idea was first raised, someone from the IETF energy working group suggested it would be a great way to model electrical power in national grids (and possibly in embedded applications). There are no doubt other real-world economies that would love a reasonable toolkit.
I believe that, if backed by YCR, possible members of an initially rapidly assembled team could include 1x very high level, successful global finance entrepreneur and executive (British; already investing in the area, keen to work together, met personally last week), and 1x pure maths + quantative finance masters (Australian) currently wasting brainpower in a conventional investment house sharing interest in the field. The nature of the problem domain is certainly more long term YCR than startup, so it's hard for any of us to dedicate time at present.