I do not feel confident in the robustness of the cooled plate.
I assume they are working on a plan C to create an above – ground deluge.
My understanding (although I do not know if this has been confirmed by SpaceX, or is entirely inference by Starbase watchers from the work in progress) is that the the top layer of the “pancake” assembly will have a large number of holes through which pressurised water flowing between the top and bottom plates will shoot upward toward the base of the first stage, both cooling the exhaust plume and acting as a sound suppression system.
Presumably once all of the pieces are in place and the water supply pipes and manifolds are connected, we’ll see tests of the deluge system and know for sure what it’s doing.
The cooled plate vs. a normal deluge system dealing with Super Heavy will be like an ultra low flow toilet meeting a sumo wrestler.