Turns out, blockchain is not actually a solution to all that many problems. All the things that make it work for Bitcoin are big downsides in most other contexts.
I could image block chain could be useful if you had digital cash off-grid, like a food truck that visited a logging camp. Collect the transactions, and then validate them when you get back to town/within signal range.
You seem to have a very strange definition of "trustless."
If you wanna trust your fellow citizen: You could go down on the street and deposit your cash with strangers walking by.
If you wanna trust luck in hashing: You should be mining Bitcoin. If you are lucky, every single attempt at mining a block will be successful. You'd become rich pretty fast.