At those speeds I would imagine the entire tire carcass would be above boiling, so assuming it was a fine-enough mist, it should vaporize instantaneously and not cause the contact patch to get wet. The problem with their setup is that it only cools the outside of the tire; the failure isn't necessarily along the circumference.
I remember an interview with Nick Heidfeld's F1 engineers back when he was a BMW driver. He had been having trouble bringing his tires up to temperature and the interviewer suggested doing burnouts. The engineer said that that would only warm up the outside of the tire and what was really needed was to warm the entire carcass through near-constant loading.
At that point we would have to start considering adding water or metal heatsinks to the inside of the tire and/or to the wire matrix (or whatever it's called) inside the rubber of the tire.
"Kimi, can you improve on your [race] finish?"
"No. My Finnish is fine; I am from Finland. Do you have any water?"