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Trust isn't a binary relationship. Computer security is hard. I trust people to try their best to not get hacked or not to get kidnapped and tortured, but alas it sometimes happens. I'm surprised no-one has mentioned that the only reason to use a block chain is to achieve byzantine fault tolerance. Casper is trying to solve much the same thing that has already been solved by Tendermint but with different trade-offs (CAP theorem trade-offs).

Well banks don't necessarily trust their international partners for example totally. Smaller banks fo instance have a lot of trouble sending unsecured wires. With the block chain it would be possible to have more trust on the amount of funds another bank has available.

Because despite the fact that they trust each other more than any random shmuck, they don't completely trust eachother?