It was rather less than 15 years ago I had the conversations with gtalk architects (who liked XMPP and left when google abandoned interoperability) that led to my opinion.
So apparently not everybody shares your definition of
'solved' - I appreciate the alternative opinion, but simply declaring it a myth is, I suspect, unlikely to convince remaining skeptics.
I wouldn't subscribe to the "15 years ago" statement, but we have figured out mobile battery use pretty well, and the respective solutions are avialable in both server and client implementations. Have a look at [0] and [1] for (slightly biased but more detailed) elabortations.
simply declaring it a myth is, I suspect, unlikely to convince remaining skeptics
It's hard to provide specific counter-arguments to anecdotal evidence repeated since back when gtalk was a thing.
The Google Talk people literally never tried to implement any of it as far as anyone could see publicly (eg. stream management, compression, client state indication, etc.). I'm not sure if it was a problem with discoverability, or if they just didn't want to, but their feedback was always that things they needed didn't exist, and then stony silence when someone would point out the thing they needed.
So apparently not everybody shares your definition of 'solved' - I appreciate the alternative opinion, but simply declaring it a myth is, I suspect, unlikely to convince remaining skeptics.