On the software side, we already have PeerTube. It’s just the logistics of hosting video are way too expensive for most people to be able to cover:

• You need drives to store all those videos, preferably in several quality and codec variants so everyone can watch them.
• You need the bandwidth to serve all those videos. PeerTube can “smooth over” the initial new upload bump by using WebTorrents, which is the least worst solution if you quietly ignore all the “but muh IP address” people, but once people stop watching at the same time, you’re back to square one.
• Transcoding requires powerful and specialized hardware. Nobody in their right mind will serve videos the same way they’re uploaded, especially with the rise of new codecs like VP9 or god forbid AV1, which you simply can’t encode on a consumer CPU unless you’re fine waiting hours/days for a single upload to go through.