They need to have your money before they can execute a trade from you, otherwise they're opening themselves up for significant fraud. If it's trade-then-send, I could sell some bitcoin, then wait a few minutes to see whether the price went up or down before I send them. If the price went up, just refuse to send the bitcoin, and execute a new sale at the higher price.

You can certainly put money in right before you execute a trade, and pull it back out right after. But that introduces significant lag, up to an hour for bitcoin, depending on how many confirmations you wait for, and several days for USD.

That said, I don't understand why people keep significant balances in these places. Keep a small amount to trade with and save the rest yourself!