Should a regulator be added to a circuit where the power source voltage matches the ICs?
Adding a voltage regulator would dissipate more power (although not much, if it's a good switching regulator), which isn't desirable in a battery-operated device. If those chips are meant to run over that full range, then I would take advantage of that. They were probably designed that way to address battery-powered applications.

If you want over-voltage protection, put a zener diode across the battery input. That would also give you reverse-battery protection and won't draw additional power (except possibly for a little leakage). Select one whose zener voltage is greater than one battery and is less than two batteries. The current carrying capability should be greater than the current capability of the battery.