I don't see how the order-making power itself would bring about the delays. The delay comes when the government or the public body tells you that they're not giving you the documents, and you complain about it. The beauty of the order-making power is that you're able to get a remedy, the equivalent of a Superior Court order, that is enforceable with contempt powers.
I don't think that concern holds water in British Columbia. I'll leave Ontario to Mr. Rubin.