Skype can send files. Skype can insert images inline into chats (that's what a smiley is...an inline image keyed to a character string.) If Skype programmers would add a button between emoticons and videos which said "emoteimages", and it opened a choose file dialog, an image file could be sent by SKYPE's existing "send file" code, and the SKYPE at the other end could display THAT image in the recipient's chat instead of a simple smiley. We could put our own, real and subtly expressed emotions into chats instead of the same image set over and over again. Emotions are personal, and this minimal effort on SKYPE's part would be a way-cool addition to typed communication.

Agree.

They seem to have simply left their plant without water just as it started to flower...

Hello...
I often use Skype to give some math lessons to friends...

It would be great if I could insert inline images generated with LaTeX...

Providing an extension to Skype to inline LaTeX-generated images would be straight forward, IFF image inlining would be possible...
That would be a great feature to be implemented!