Besides automobiles, I'm not aware of any personal hobby or activity that is mandated by law to carry liability coverage. Not even an activity like hunting with firearms require personal liability. I cannot envision a world where flying a drone for hobby would be mandated by law to have coverage.
If you’re in the United States, and you have an income and or your net worth is more than your UAV is worth, why would you not have liability insurance, on every thing (umbrella policy)?
If you bean somebody, no insurance, they own you in USA, maybe other countries.