SpaceX has the potential to become by far the most powerful company in the world, and more powerful than any government off-world.
Currently, logistics and information are the most powerful things for a company to control; and SpaceX will have a monopoly on offworld logistics with Starship, and also own Starlink which will be the world's most valuable piece of informational infrastructure.
As long as it's a privately owned company headed by Elon Musk, SpaceX can be expected to act responsibly. But private companies are dictatorships: No matter how they're run, when the head dies or vacates odds are that their replacement ends up being malevolent.

Imagine it's 2030 and everything has gone as planned for SpaceX. They have 42,000 internet satellites providing a huge portion of Earth's bandwidth, regularly ferry people to Luna and Mars, and ferry a smaller number of people back.
Elon Musk is in LEO waiting for refuelling, and Jeff Bezos wants to show him his latest bootlegged rocket, getting as close as possible to Musk's rocket. The bootleg malfunctions, colliding and killing them both in a huge explosion.
So what's then done with SpaceX? Virtually all billionaires and boards of massive companies are inhumanly greedy. You have to assume that whoever controls SpaceX, either an individual or a group, will be greedy.

Starlink and Starship don't raise massive red flags for anyone. Critics of Elon Musk don't expect much, fans of Elon Musk take no issue with how powerful such projects could make him because he's "the saviour of humanity". But remember, however much power Elon Musk acquires, all of it gets handed to another party when he dies.