> The raison d’être of SEC is to protect regular mom-and-pop investors

That's not the sole reason. They (should) also enforce a fair even playing field by preventing market manipulation (e.g. how Elon was tweeting about stock prices) and a few other things to "facilitate efficient markets and the formation of capital".

> Why should SEC rules apply?

Because private companies still fall under the jurisdiction of the SEC? See e.g. Theranos.

> On what legal basis can you force a private company to divulge its financial details?

On the to-be-created legal basis that aims to prevent bubble formation and the resulting fallout to the wider society?

> Would you be happy if you, as an individual, have to divulge your account statements if your own net wealth reaches one million?

Sure, why not? It's not a totally unheard of idea. In Norway everyones salary can be looked up.