Reddit seems to think that Starlink is already serving users via sat-to-sat optical links https://www.reddit.com/r/Starlink/comments/xsupcn/laser_link...
For extremely latency sensitive applications, I guess they will (e.g. for trading and real-time communications), but for everything else that can wait a few more milliseconds, I'd guess that the operational overhead and reduced reliability will never be worth it, especially if fiber already exists on the same path.