It is why the US military keeps a short-term stockpile to protect active personnel (though not enough for dependents or the public), why small amounts are kept at every nuclear plant for worker protection, and why some countries in Europe, Asia, and the Middle East stockpile KI for civilian protection.
As part of its emergency response planning, the NRC has conducted two studies on the dispersion of a radioactive plume in the event of a serious accident. Both predict radiation dose levels to the thyroid that could reach 100 times "safe" levels among exposed individuals at 50 miles from the release. And both predict that dangerous levels could be seen for 200 miles downwind.20
But it is encouraging to note that the World Health Organization has noted that "except for thyroid cancer" no increases of other cancers attributable to Chernobyl were found after 10 years. This is why there is near unanimous opinion that a sufficient national stockpile of KI would be an extremely important medical counter-measure for protection in a nuclear emergency.
Unfortunately, this stockpile does not currently exist.