What I'm asking is, why do people care? It can't just be because other people do. It takes a significant number of people to care for no good reason before it makes sense to care just because other people do.
It's simultaneously possible to be against Musk continuing to do things like that and be against the media continuing to cover it as though it should matter.
As to why other people care, people love celebrity gossip, especially “bad” gossip. It sells ads and clicks and generates conversation. At some point, it becomes self-sustaining. I agree that it’s terribly uninteresting in general to me.
Note that I believe his erratic and lightly considered Twitter posts are one thing (ignorable) generally, but I think the $420/“funding secured” tweet to be much more likely legitimate news and quite likely of the “watch me burn these shorts!” securities fraud variety. There is an extent to which such legitimate interest in that tweet brings interest in his other tweets to understand whether the CEO of a many-multi-billion market cap company is prone to communications that put his company/others’ investments at risk. I suspect that extent is less than what is being covered, because it’s a justification for why (largely) respected financial news sources are now able to cover salacious details of his private life with plausible explanation as to why.
He could have pursued Tesla in a quiet, modest way. Instea of making bold predictions, he could have underpromised and overdelivered, letting results do the talking. He could have stayed out of the limelight, remaining just another CEO.
We all know what he did instead. And that surely got him a low cost of capital and a ton of free PR, so it's reasonable to argue it was the right business move. But having put himself in the spotlight and made it all about Elon, I don't think it's reasonable to claim it's unfair that he's now in the spotlight.
If we're being purely rational, people shouldn't care about the technology genius mystique, and they shouldn't worship high-profile business executives. But they do, and Musk grabbed that with both hands. He can't do that, glory in the upsides, and be upset about the downsides. It's a package deal.
It's more probable than not that he should take a short vacation (or some other kind of break) and stop shit-posting on Twitter. Those aren't mutually exclusive options.
Temporarily taking a slightly lower profile and spending his focus on things that actually matter to his companies (cave divers, pop stars, and short-sellers are not in that set, IMO) would probably be good for everyone/everything that Musk cares about.