Those on 3g will have to wait ages for the video to buffer. Those on an old device won't be able to play it at all if you used new codecs. Users won't be able to select playback quality, and on a slow connection, they'll get endless buffering.
You'll have to come up with your own systems for counting how many people viewed the video and which bits they bailed out on. You'll have to reinvent caption translations and go to extra effort to get captions working at all.
Self hosted videos have mostly died for the above reasons.