Hotel chains want you to book directly through them because it costs them less to make a reservation themselves than it does to pay a commission to Expedia or other online travel sites (or travel agents).
Hilton tested a small discount in a handful of cities restricted to Hilton HHonors members. The discount wasn’t great, about 5% (and so generally more expensive than AAA rates), but it was more about the model than the amount.
Today Hyatt introduced member-only discount rates and in some cases they’re bigger discounts than what Hilton and Marriott are offering, but still not better than AAA rates. And they’re not available worldwide.