Since YouTube is not profitable, a competitor that can actually be successful, will need to work towards a lower cost way to distribute the content.
A torrent based YouTube competitor can work well if made user friendly, especially since the largest cost aspect of a service like YouTube is the cost of distribution, and not the storage.
While storage can be expensive, it is not as expensive as the infrastructure needed to handle millions of streams simultaneously.
On the other hand, there are some sites which can release an anime fansub on a single server (1 server with a gigabit connection, seeding thousands of torrents stored on a SAN), and within an hour, well over 100,000 users can have a copy of that video even if it is a large 10GB+ 1080p 10 bit. One issue with services like YouTube, is that it is not profitable even for google, they instead use the platform to expand their audience in order to increase the value of the ads that they can put in other locations. This is all due to the internet not really being designed to function this way. It is far more efficient to download videos where if the segments of the download are downloaded in order, if it goes fast enough, you can download and watch at the same time, and if not, you wait for the download to finish (if the file support partial downloads). As long as a reasonable number of users upload as they download, the network scales well.
The benefit of bittorrent is that it requires surprisingly little infrastructure to host petabytes of content. With intelligent seeding where users with the best initial ratios get pieces first, you can often see a torrent with 1 seeder that was just released, along with 20,000 peers, still allow you to download at 100+Mbps, especially on networks where poor ratio peers cannot connect to seeders early on.
The other benefit of the network is that they are extremely receptive to a sudden influx of peers, as more join in, they have more throughput to share, and as the initial rush of viewers dies down, and the number of seeders drops, the few users that occasionally stop by to download the torrent, will easily be handled by the remaining seeders and the primary server. This is why some PC games use a torrent based updater, it allows an indie studio to push out a 500MB patch to a 100,000+ players, using a server on a gigabit connection.
The area where they can beat YouTube, is in the area of quality. For example, YouTube's compression is always a topic of complaint since even they need to keep the infrastructure for handling streaming under control. If torrent based distribution is done, someone could deliver a video that is 4K 200Mbps data rate. The major channels can have HD-8K+ streaming at similar quality to youtube, while smaller channels can just have standard definition with torrent based HD to 8k+ content. That will allow for far less distribution infrastructure as they will only really be dealing a small number of channels, while the vast majority will use torrent distribution. The infrastructure will just be storage heavy but with only a tiny fraction of the distribution infrastructure, thus reducing the cost of the most expensive aspect of the media platform.