>There is a huge amount of vested interest in persuading people bitcoin or ethereum require no trust in third parties.
It requires trust that third parties will act rationally in accordance with the incentives provided by the system, which is very different from trusting someone to custody assets for you.
At a larger level it requires trust that people will continue to see BTC/ETH/etc as being worth something, but that isn't a unique problem to blockchain based digital currency solutions.
Sure but is a rationally acting financial institution operating in line with the incentives of the system they operate not also inclined to do everything to keep your money safe?
I think the key phrasing here is "the incentives of the system they operate" — it isn't completely unfair to say that large financial institutions have had a hand not just in operating, but in creating the system. They act according to broader financial incentives and are constrained by regulations (so disincentives), and their time horizon is much longer than the tight feedback loops produced by a blockchain. Their disproportionate influence over the financial system coupled with a feedback loop in terms of consequences that, compared to blockchain, is glacially slow and basically toothless, effectively gives them a ton of latitude to do shady stuff with your money.
It requires trust that third parties will act rationally in accordance with the incentives provided by the system, which is very different from trusting someone to custody assets for you.
At a larger level it requires trust that people will continue to see BTC/ETH/etc as being worth something, but that isn't a unique problem to blockchain based digital currency solutions.