Ethereum's ecosystem is trying to solve a lot of this. For example, the 0x protocol allows exchanges (in the 0x parlance, 'Relayers') to forego holding customer

Ethereum's ecosystem is trying to solve a lot of this. For example, the 0x protocol allows exchanges (in the 0x parlance, 'Relayers') to forego holding customer assets (and therefore also avoid KYC/AML/etc.). They take a fee for creating the UI and matching orders, but the matched orders execute as smart contracts on the Ethereum blockchain pursuant to the open 0x protocol. Multiple relayers will compete for business using this protocol. The first relayers will be launching soon (e.g. Radar Relay).