The CEO of SpaceX owns Twitter.

I'm aware. What does SpaceX gain from the exclusivity?

The CEO of SpaceX owns Twitter.

Im sure SpaceX's investors love being used to promote a single private social media platform. Sounds like another case of the CEO enriching themselves to the detriment of investors.

There are hypothetically advantages. The affiliated company would be more inclined to promote them, so they could get in front of some people who otherwise might not have seen it. Conversely, a company that competes with the affiliated company might be inclined to do the opposite to avoid promoting a competitor's businesses, so the countervailing costs of exclusivity are lower for their company in particular.

They also might be wary of platforms like YouTube which host "Elon Musk wants to give you Bitcoins" scam videos, which Twitter has a stronger incentive to be aggressive in removing because of who owns it, and then there is value to the company in being able to say "none of the YouTube videos are legitimate, you can only see it here."