What makes it so that this kind of precision is required? I have little knowledge of the physics behind it, but a few decades ago, a local university had an open day where they bounced lasers off of a retro reflector on the moon to measure the distance: https://en.wikipedia.org/wiki/Lunar_Laser_Ranging_experiment...

The moon is 700 times farther away than the starlink satellites (or twice that, if you consider the bounce), so I find it hard to imagine that it would be impossible to communicate with much closer satellites over laser when both sides can have an active transmitter.