The easiest solution would be to add a check into the video bbcode function which checks if it's youtube, vimeo, or an html5 video
But that would require adding more and more code for each host we wanted to support. And relying on 3rd parties to host content is a recipe for link rot. The ideal solution long term would be to make a file hosting service for wetfish which automatically rehosts video files from 3rd parties. It could use youtube-dl to download the files, which already has support for hundreds of different sites including YouTube, Vimeo, Twitter, Instagram, Facebook, and SoundCloud.
Seriously, youtube-dl is one of the best open source projects, I will never stop shilling for it
http://ytdl-org.github.io/youtube-dl/