One of the main reasons is that you can see the site's funds. It's all public. Most of the sites share their addresses, even if they don't, you can basically find it by just checking a few addresses on the blockchain. This is especially important when checking out, for example, an exchange site. If the exchange does not have even 1 BTC but is advertising themselves as the biggest and the best exchange, that should raise some flags. So, long short story. Transparency, whether they like it or not is probably my main reason.