Support Screen Capture per W3C Specification
The Screen Capture (or screen share) specification  allows websites to obtain a MediaStream of the user's screen, given permission from the user.
Firefox has implemented the feature per specification (no longer requiring a whitelist ), while Chrome only allows the feature when initiated from an extension.
 Specification: https://www.w3.org/TR/screen-capture/
 Firefox re:whitelisting: https://wiki.mozilla.org/Screensharing
Screen Capture API is in development. https://developer.microsoft.com/en-us/microsoft-edge/platform/status/screencapture/
Oleg Dolotov commented
Why it this idea was posted only few month ago and there is NOTHING that Google (and Bing actually) can find about screensharing in Edge. Chrome has it for ages. Definitely a must have.