I always compare between the hotel's site, TYP Portal, and 3rd party booking agencies. Yes, you're right that sometimes it costs more through the TYP portal. Availability is also cramped compared to other booking engines.
But if the hotel's own site, or special rate code/promo, is cheaper -- you can call the concierge and have them book the rate you want direct with the hotel. Just feed them all the details ahead of time.
That is a pretty good benefit since you can also usually append your loyalty number if its a hotel that has a program.
The drawback to booking through the concierge is that you have to wait for the statement credit, which could be an issue if you were cancelling the card in between travel time and credit posting time.
An additional consideration to using the concierge is that you can't use TYP when booking through that channel. This is more applicable to the small subset of holders who combine Premier TYP uplift on hotel bookings with the Prestige 4NF. I have an upcoming booking I've been watching for every day hoping that they will release something to Expedia/TYP inventory....but we're starting to reach the danger zone (for pricing hikes/availability) so I might have to cave in a couple days and just use the concierge manual booking process.