A voltage regulator would keep the output of the alternator at a certain voltage.
The alternator might be able to produce 18 volts, but that is too much!
You would want the voltage to be around 13/14 volts when the alternator is charging.
And a voltage regulator would be like a water valve. It would let more electricity through if needed - say you turned on the lights and A/C. Or less electricity through if you turned these off.
Since it is like a valve, if it broke, it could always be on full blast and too much voltage is getting through. Or totally off and no voltage is getting through. Or it may work when cold, but not when hot.
Test with a voltmeter.
The battery should read 12 something volts with just the ignition on (not started).
Then start it and it should then read 13/14 volts at the battery. This is the alternator kicking in and charging the battery.