The way I understand if your solution would become popular, the law can come after you to provide a log of messages in plain text.
Also they will have the legal power to force the popular operating systems to enforce generic keylogging/packet capturing and whatnot.
I don't see how they can come after anyone who's using a specific protocol [0] by law. Expanding on this thought: if Chat Control passes, it will just be the death of social media as a chat platform. People will swap to something more rudimentary where it can't be enforced. Primary reason why being that it simply will be so much faster/more convenient than the apps which are forced to use chat control.
The same reason as why streaming services are being ditched in favor of piracy will happen to social media.
[0]: https://en.wikipedia.org/wiki/IRC
You think too much about the Regular Joes/Janes. No-one will care for more than 2 weeks apart from tech people