I think it makes perfectly good sense for SpaceX. They've always made it clear that their real business goal was colonization of Mars based on optimizing the cost of transport to space via reusability and design for manufacturability. Everything else they've done is basically just a way to monetize their current space travel capabilities in service of funding the design and construction of what they really want to do. Making Starlink as profitable as possible was never a goal, just a way to make some more money off of their incredibly low launch costs and probably also develop technology for communicating between ground and spacecraft. So why not launch a competitor too? It's just more launches and more funding for them.
I have a nice dream that Elon will build rocket and space enterprises, get them profitable, only to break them up and go public to allow them to be independent corporations and allowing real competition to begin (plus remove all his other business interests from each companies mission)
He could still rake in cash from their owned shares it would just be them creating a real public space sector for the good of humanity. This will never happen ofc, but I can dream.
You can't rake in cash from owned shares if they don't pay dividends and I don't think he has much interest in selling his shares. He's previously said repeatedly that SpaceX won't go public until there are regular flights to Mars, which will likely be after his death.
That sounds like it might be even more profitable, but he already has more money than he knows what to do with. Besides, that seems less fun than being absolute dictator of mars.
He has a lot of wealth, but he doesn't really have that much "money". He can't re-invest in SpaceX by selling SpaceX and then buying SpaceX again... He could diversify away from SpaceX and Tesla, but he doesn't seem very interested in that.
