[Klojum]

but it is true that nobody wants a video player that doesn't support it.

Yes, you are exaggerating. And yes, it would be nice to have Chromecast onboard in Kodi, but .. it would also be another piece of software to implement, test and maintain.

Knowing what TeamKodi's resources are what they are at the moment in terms of available developers (support for 'pyChromecast' would have to be there for all Kodi supported OS'es, not just Windows as in your case), and, with plenty of Kodi users already having alternatives available, it's not something that is in the immediate pipeline. I have 2 Google Chromecast dongles and a Nvidia Shield that supports Chromecast and they do an excellent job.

[jjd-uk]

Kodi does however support the much older and more universal UnPnP protocol.

[j-m-s]

When my TV is on and I watch a photo or video on my android phone, I just touch the "cast " icon and the photo or video is shown on the TV.
I would like to have the same in Kodi, so that I can send pictures and videos from my phone to kodi.

[jjd-uk]

You can, install something like BubbleUPnP on your phone and use it to cast to Kodi via UPnP.

[j-m-s]

You can, install something like BubbleUPnP on your phone and use it to cast to Kodi via UPnP.

This is possible but this casting is not offered from android within the picture gallery or video player.