There are other considerations at play besides the 5X. For example, perhaps the point/mile earning would have been higher had you booked the room with a Chase Sapphire Reserve (3X) via one of the various sites that give bonus miles for bookings (e.g. RocketMiles, Kaligo, etc.). Not always the case, but you should always check.

Also, most major OTAs have 10-20% off coupons floating around at any given time, but they don't work on every property/brand so YMMV.

Not trying to be a downer, and indeed there are great deals to be had at Amex Travel. I recently made a booking for a London hotel that was over $40 less per night via Amex Travel and ineligible for OTA coupons on competing sites. Also did not appear on the aforementioned miles-for-bookings sites at all.