Comment by WorldMaker

They sort of already exist, many emoji are turned "on" (colorful presentation or Emoji Presentation) with Variation Selector 16 [0] and many can be forced "off" (monochrome presentation) with Variation Selector 15 [1].

(Not all fonts handle all variations, though, in both directions.)

[0] https://codepoints.net/U+FE0F [1] https://codepoints.net/U+FE0E