I see no reason why the search feature within YouTube couldn't return videos that people were hosting on their personal sites or on competitors to YouTube (including Twitch VODs and livestreams). Even subscriptions and recommendations could work across platforms.
YouTube could still run adverts in/on the videos, and the revenue from that would be split with the site where the video was actually published. For a greater share of the ad revenue, YouTube could also offer to stream (a copy of) the video from their own servers.
Even if sites (or Multi-Channel Networks) had to pay a $1000 fee to be included in this system, and YouTube kept its rules about moderation and demonetisation, it would still greatly improve discoverability and hopefully competition generally.