> for example popular messengers can send and receive text,
Your messenger isn't sending tens of megabytes for every message.
> metadata and blurry image previews just fine.
One might wonder why they don't just send the 4 MB JPEGs instead of those down scaled to hell previews if they work so well.
> . In some cases even voice calls are possible
Not only kilobytes of data, but kilobytes of data where transmission errors can be completely ignored. I have been in enough VoIP calls to notice how "well" that works in bad conditions.
Everything points to putting websites on a diet being the correct solution.
> And if the connection drops, then it almost certainly won't recover and full page reload is necessary.
I would consider that a browser bug. No idea why the connection wont just timeout and retry by itself.