This would suggest that the risk should be linear with radiation dose. But cells have DNA repair mechanisms. If a person receives a very large dose in a short amount of time, it makes sense that the repair systems might be too overwhelmed to fix all the damage that has occurred. Of course, the repair system isn't perfect, and some small fraction of damage will be permanent. This suggests that LNT should be true for small doses, but the harmfulness of radiation per particle should increase at larger doses.
A few consequences if that's true:
Depending on how the constant coefficient is determined, a fully linear health risk model will tend to overestimate risk at low dose rates, but underestimate at high dose rates.
This also suggests that radiation concentrated in a particular spot on the body is particularly dangerous. The cells in that location will be bearing the brunt of the radiation dose, so their repair systems are more likely to fail. So inhaling a bit of plutonium dust means you're in for a worse time than absorbing an equivalent dose spread out over your body.
Of course, whatever health risk model we choose, it should also be applied to the regulation of coal plants, since they put radioactive isotopes into the atmosphere as a part of their regular operation.
Isn't it true that the proportionality coefficient for LNT was calculated using cancer rates for atomic bomb survivors? The dose for them would be very rapid, and there would be little time for enzymes to be produced. This would explain why such a valley didn't show up in that particular set of data.
Nuclear fans like to complain about the LNT, but I don't think they're really thinking this through.
In a nuclear accident, most of the population exposure will be a minor increase spread across a vast population. At those doses, we basically cannot check whether LNT is true or not -- the small cancer incidence it predicts is statistically invisible against all the other causes of cancer.
So foes of LNT want to say "we can't show LNT is correct", which is fine, but then they say "so we must assume the actual effect is smaller, perhaps zero", which is not fine. The evidence doesn't support that second step, and this is not a court of criminal law where radiation must be presumed innocent unless found guilty beyond a reasonable doubt. One might very well argue that one should take a precautionary approach, which is to assume that low level radiation has the worst effect it could have that is not ruled out by evidence. This would imply even larger threat than under LNT.