It is impossible to remove trust requirements from all types of transactions. For example, ordering a product online. What if they don't ship? Crypto-currncies do a great job of reducing the amount of trust that we need but I don't think it can be eliminated completely.

For example, there's no way to trade with leverage on Ripple. In fact in the Ripple wiki they give plenty of reasons why an off-ledger exchange can be superior to Ripple's built in exchange.