First off, I would like to debunk your claim that black text on white background is stressful on the eye.
Using white text on a black background is actually the most possible stress you can place on your eye
Forcing users to fixate on the white text for a long time can strain the user's eyes. This is because white stimulates all three types of color sensitive visual receptors in the human eye in nearly equal amounts. This makes reading white paragraph text on dark backgrounds stressful on the user's eyes.
White also reflects all wavelengths of light. Because the words and letters in paragraph text are compact and close together, when white text reflects light, the reflected light scatters and runs into neighboring words and letters. This makes the shape of the words and letters harder to perceive, which affects the user's readability. Compare that with black text, where the black absorbs the light around each word and letter, making them easy to distinguish.
More reading from UX.stackexchange (same conclusions): White text on black background, What is the best color combination for on screen reading?
Secondly, the issue of requesting Stack Exchange provide an implementation of user specific css styles. This request is pretty demanding, both of the team that spends many hours maintaining and improving the exchange, and on the servers which would have to serve all these new stylesheets. Stack Exchange is all about speed, almost to a fault (but not, because we all love the speed). In fact, recently the entire site's css was trimmed to get those extra few milliseconds for users.
There is nothing preventing you from running a user script to accomplish this or making a browser extension so if you really feel that strongly about the color scheme then I suggest you implement it locally.