Why are lights on 15 amp circuits and receptacles on 20 amp?
Breakers protect wiring and connections. Most lighting circuits are done with #14 wire, which is adequate for the duty it performs. To prevent overheating (fire risk), 15A breakers are required by code for most circuits using #14 AWG wire. Lighter wire and other components are less expensive and easier to work with.

Many power tools, appliances, and other devices draw at or above 15A at startup or under load. It's often desirable to have more current capacity there than you'd need in a lighting circuit. 20A circuits are typically wired with #12 AWG wire to handle the additional current safely. 

Simply put, each circuit has a different purpose. It's not just about short circuit protection, but available current load.