One thing that could be done is for the aggregators to require a video publisher to post a bond. This could apply not just for the EU copyright rules, but for any other weird country specific laws. If the video publisher posts something that breaks the law, then the money is removed, the regulator paid, and the publisher's license revoked.
This would allow a marketplace of editors. Someone who was making, for example, cooking videos, probably wouldn't have a couple of million dollars sitting around. Instead, their videos would be syndicated through an editor. An editor could make their own decisions on revenue share (if any at all) based on their own judgements of legal risk vs revenue opportunity. This could mean live streamers all have to go in to a closely monitored studio instead of doing it from home.
In a way this is similar to how the old network TV or print periodical marketplace worked, but adapted for the internet. Network TV had to pay big fines if someone said fuck or a nipple was broadcast live. Thus, they assumed legal liability for their guests behavior.
This still doesn't solve the core issue that the Youtube CEO described, which is when a bunch of people claim copyright on the same video. Solving that probably requires clawback provisions over lost revenue from making fake claims.
I don't think this approach would be ok in the United States, but it seems reasonable for the EU, China, and so on.