The particular color of green used in greenscreens is used because it is not a natural color found in nature.
Our photog poster can use Photoshop and selectively select areas with white or any other color to key. And you can too - if using a static image for a background. Videographers using a video background, at least, those of us trying to key with our NLE's, cannot select areas to key by color without resorting to matting, which complicates the process and since you'll likely have movement, you'll need a moving track matte which may grind your NLE to a near halt when combined with keying.
If you key to white without limiting the keying area, the white of people's eyes and other areas will become transparent or partially so. There is some white in almost everything.
Keying with a greenscreen is difficult enough (at least, if you want really good keys so your effect comes off well), so you may not want to make it even harder.