Hey, thanks for the suggestion, but we don't have plans to implement that in a foreseeable future due to challenges you have outlined yourself in your post.
It would require a significant effort to address them, plus there are a lot of third-party video hosting services that you could use if you wanted to share a screen capture on this forums.
I know this is not ideal, but it's a viable workaround for this problem, I think.
Best regards!