Fascinating stuff. The problem with your conclusion (“Just pick up the phone and call the front desk”) is that front desk people … and reservations people … historically have been trained *NOT* to offer the cheapest possible price to callers. You have to keep pushing them (“Can you offer me a better price?”)
So I would recommend a small change in your suggested approach:
(1) Find the best price you can on an aggregator site
(2) THEN call the front desk and negotiate for a better one.