Amp Breaker

I thought it would be the amp of the alternator. 60 amp alternator = 60 amp Circuit protection. Is this wrong?
It is wrong.
Take house wiring for example.
If there is 14 gage wire in a circuit, the circuit gets a 15 amp breaker or fuse.
If it is all 12 gage wire, then a 20 amp breaker is allowed.

My guess is the code doesn't worry about the lamps and fixtures themselves because they are outside of the walls and you will notice the bulb go out.

The '60 amps' is just a manufacturer's approximation of maximum current at some voltage. Kindof like Holley's 750 is an approximation of cfm at 1.5" (or something like that )