This is a temporary defect of the Internet, but there's no reason why video should be handled differently than text or images.
When you set up your home web page, you publish text and images from your server. Similarly, you can be able to publish videos from your server.
The reason why services like youtube exist, is because video files are big, and therefore ISPs complain about the bandwidth used (without monetary compensation) by their users publishing them, on one hand, and on the other hand, transmission of those big files to, sometimes, a large number of recipients, taxes the resources of the network (ie. the network is currently under-dimensionned), and the solution proposed is CDN, content delivery networks, which big companies like youtube and vimeo are able to contract for a good price. There are several scarcities at play here, and eventually, there's no reason why they should persist.
- increase of the network bandwidth everywhere should make it easier to publish big files such as video from anywhere to anywhere,
- some CDN features could be implemented in the network, in a net-neutral and general way, but this would be a big philosophical change from the principle of the Internet, where the end-to-end principle is of first importance.