Earlier quoted context omitted.
I don't see pixel-level precision being hard. As for color-correction, I would bet they have settings to allow you to adjust based on your monitor.
Doing color correction based on monitor colors would be impossible: sometimes you adjust, for instance, RGB curves for one specific layer. It could mean that half of the screen is changing with every step of the slider, and you want exact color, immediately.
For one, doing client-side color correction (for example with WebGL) is technically possible. It's probably not in this solution, but let's not use words like "impossible" unless they're actually impossible.
But more importantly, I think you're just complaining about latency, but then you're using the phrase "impossible."
EDIT: I thought you were talking about gamma correction and the color space of the display, where the program running on the server wouldn't know about the gamma and color characteristics of the monitor on your current browser. Thus, "monitor settings." But no, you're just worried in general about whole-screen fill rate latency. Again, I think using terms like "impossible" is hyperbole. It will be fine for some users, and not for others.