1) I am not a medical researcher. AFAIK, medical research on health impact of PWM-like display flickering has been insufficient for both short-term and long-term studies.
2) The change from CRT displays to modern displays, of which some flicker, is comparatively recent from the view of potential long-term impacts of those modern displays with flickering. Everybody was aware that CRT displays flickered so the common sense and medical recommendation was to use them together with ambient room light to reduce the likelihood of bad long-term impact on health of the eyes.
3) Due to (1) and (2), for modern displays with flickering, anecdotal evidence as follows by individual, affected persons prevails and so far is limited to short-term impacts. Different users have, or have not, had some. Of the affected users, impacts can occur immediately, after a few minutes or after weeks or months of use. Experienced health issues have been headache, acute health problems of the eyes, lack of concentration or general unhealthy feeling. While some users incur health problems only for low PWM frequencies (say, below 1000 Hz), some other display users (including NBC forum users) also incur health problems for high PWM frequencies (such as 250,000 Hz).
4) In my own experience with flickering light of any source (including neon tubes, flickering outdoor xmas lights, indoor light blinking due to a defect etc.), it causes stress and lack of concentration. Besides, long nearby exposure causes acute health problems of the eyes. Therefore, I have avoided all modern displays with flickering because I expect similar short-term health problems and, due to display use for several hours per day, additional long-term health problems especially of the eyes.
5) Double-blind experiment and whatnot: Scientific studies would be better than none. However, the most basic studies should come first: Roughly what percentage has already experienced short-term impacts? How much less choice among hardware do those have choosing to avoid flickering displays? Are manufacturers held liable for causing health problems of some users?