Linear no-threshold actually maps fairly well to skin cancer which is a direct proxy. What differentiates things from a slap is each event is very energetic, and operates independently on each of your 30 trillion cells. Like shooting at random they mostly don't hit anyone, until the one just happens to be in the wrong pace.
At a lower level their are many systems that both cause and reduce the risks of cancer. However, over a lifetime the odds of getting cancer end up being fairly high and most people end up a single mutation away from cancer. At which point every even is just another roll of the dice.
1) A slap on the wrist is highly energetic, and speaking from an understanding of basic materials physics it seems very likely that it damages cells, ligaments and bones. We just heal from it very easily because the damage is completely trivial.
2) Skin cancer can't be reasonable proxy. I live in Australia, and it is well-known here that skin cancer is frequently caused by sunlight.
Now the dose of radiation you get from sunlight is huge. On a typical day, you are exposed to enough radiation that you can detect it as heat (ie, we associate heat with sunlight). I've only ever been exposed to enough artificial radiation to feel heat in dental X-Rays. The LNT model is going to be operating at much lower levels, because the theoretical damage is being done to people who cannot detect it.
That link alone is surely going to overwhelm the effect of tiny doses of radiation and make it impossible to detect low-threshold increases.
1) Cells are elastic and suspended in water which allows them to survive what you might think of as extreme trauma. (Ever seen someone hammer a nail with a glass bottle filled with water?) Combine that with the elastic nature of connective tissue is what allows you to for example jump without killing off of the cells at the bottom of your feet.
2) Sunlight is EM radiation like X-Rays. However, the vast majority of the energy is harmless and and even UVA / UVB is limited to the top layers of skin. But, as far as those top few layers of skin are concerned it's like your constantly getting very weak X-Ray when standing in sunlight making it a great proxy for low level radiation exposure.
At a lower level their are many systems that both cause and reduce the risks of cancer. However, over a lifetime the odds of getting cancer end up being fairly high and most people end up a single mutation away from cancer. At which point every even is just another roll of the dice.
Net result, observed results look rather linear.