Fingerprinting can take care of the recompression problems.
Remuxing is a hard problem, as it can easily take people out of context, at the same time it's very important to summarize the videos, as people have limited time.
Right now what I see though is that Facebook/Google/Twitter aren't even trying to do the bare minimum end-to-end authentication that Whatsapp/Telegram/Signal already does (create a private key on the end devices, and sign the content to verify the authenticity of the publisher).
Requiring HTTPS was a great first step for tech companies to protect people and from ISPs. But they do nothing to protect people from themselves being compromised (the Twitter incident was a great proof for this).