Examples of such assumptions: Bitcoin transactions in the blockchain can never be annulled, removed, or hidden from view; Ethereum contracts cannot be modified or voided by third parties (e.g. a judge).
Unfortunately, removing immutability from the blockchain turns it into something that isn't more trustworthy than any other kind of ledger -- so what's the point of using it? So, I don't expect this kind of technology to be viable for mainstream banking, or any other use case where the real-life legal system gets involved.