Starlink is capital-intensive and untested as a business proposition. This keeps the risk walled off from SpaceX and lets them raise without diluting ownership of SpaceX. (It also means guaranteed profit for SpaceX from the pockets of new investors.)
Not sure why they'd go public instead of raising the capital privately, though.
Also, perhaps Musk thinks that having public retail investors is worth it. After all, even though they contribute approximately 0% to Tesla's funding, retail investors and owners generate approximately 100% of the hype, online content and general proselytizing. That is, someone will have to defend Starlink from accusations that it has ruined the sky, and Musk alone can't do it.