You've misunderstood the possibilities -- it's not just "store everything" or "trust someone else". You can download all of the headers but none of the data (resulting in a 27M ETH blockchain today), and then download the full blocks that you need on-demand when you want to query transactions, with no loss of safety. (If someone lied about the block contents, they'd fail to match its header hash.) This is what happens in Ethereum's "light" sync mode:
That simply isn't true. Accepting a blockchain blindly without validating is the Bitcoin SPV model. In ethereum it amounts to an undiversified risk that the two mining pools needed to constitute a majority hashpower (ethermine and f2pool) will not violate the protocol, or-- if you are accepting state with few confirmations as final-- that _any_ miner will not violate the protocol.
Headers are fingerprints / unique hashes. If someone else has already derived account balances to a particular point, it may be enough to avoid duplicating the chain.
https://github.com/zsfelfoldi/go-ethereum/wiki/Light-Ethereu...