You will probably consider these as "financial schemes", but having worked in finance for many years my impression is there are a number of problems in financial infrastructure that are extremely annoying and costly at the moment which could be much better addressed with blockchain based solutions. Blockchain is not the only way you could solve them, it just has the potential to be much better.
One example: Trade reconciliations. Lots of things (eg swaps contracts) that trade "over the counter" (not on an exchange) start off crazy bespoke but over time end up being largely standardized. So these days if you trade a swap, the contract is a standard contract called an "ISDA Master" with essentially a one-pager referencing the isda master filling in the blanks in the standard contract - what the legs and key numbers are, who is long vs short the legs etc. 10s of thousands of these are traded every day.
In order to settle these so can people actually start paying each other money, there needs to be a reconciliation (ie I need to agree with you on the contents of the one-pager so we both know exactly what we are both holding). Because the two sides don't trust each other (they are adversaries in the market), both will have entered the details of the trade in their own systems as they understood them and there will be errors and breaks and things are hard. Armies of people and systems are employed to solve this problem. If there was just a central database it would all be so much easier[1] and this whole reconciliation problem would go away, but how do things get into the central database in the first place and how do the participants trust that the record there is good? Well, you can see you would still have the same reconciliation problem.
Blockchain could resolve this by having a single definitive contract record stored in a trustless fashion. You could make it so if both sides put in the same details the trade is matched and otherwise both sides get the trade rejected until they can resolve. It becomes trivial because you have a database that can be shared without trusting any central party. There are trusted central parties (eg clearing houses) in these systems by the way, but they behave as another counterparty so they don't solve the matching and reconciliation problem described above. You still have to match the two potentially-conflicting versions of the real contract for the clearing house to novate (step into) it.
Now are there other ways to address this problem? Of course - they are doing that now. They just suck.
I'm sure other industries have similar issues around reconciliation between parties etc that would work the same - I'm just not personally familiar with them.
[1] It would also be far easier to report these trades to the CFTC btw so that's another pile of cost that could get taken out by such a solution.