The power used by a fluorescent tube is not linear to voltage, the tube would without the ballast run away and allow a huge discharge.
The same with a non switch mode power supply, a 12 volt output from a transformer, diode, and capacitor into a 7812 voltage regulator would produce no heat from the 7812, but increase the voltage to 14 volt and the regulator starts to produce heat, depending on the load, so again power used not linear to voltage.
Eric, there is a major difference between a series regulator and a tube ballast. The series regulator acts exactly like a dropper resistance, deliberately wasting the surplus energy.
