It could be the Tanavast's focus isn't on the Heralds because by that time he "knew" that 9 of the 10 betrayed the oathpact. Or rather, are currently choosing to not uphold it.
So, the key may be this. The Heralds "hold out" for torture as long as they can while dead. When the last one renounces, they "rebirth" on Roshar and the desolation comes. It's even possible that originally the *only* method to stop a desolation was the Heralds. The Radiants seem to be a relatively "new" addition in that the most recent desolations contained Radiants.
The Radiants themselves may be enough to stave off a desolation as champions of Honor itself. Also if Tanavast is correct, in that Odium realized that by *not* having frequent desolations and "laying low" for, well, 4.5 millenia, the existing Heralds would be lost to time, and the Radiants would likely implode. He doesn't really need champions or follow the structured format of the contest between Honor and himself. Rayse has killed Tanavast. Now that he's recovered, he can do a desolation relatively unopposed.
Well, imo anyway.