Is there a good reason NOT to reuse the power cord when replacing my electric range/oven?
A nearly 40 year old power cord is going to be nasty. Dust, grease, possibly cracked insulation internally, possibly asbestos insulation if the "original" cord was itself recycled. All are fine unless you disturb the cord. Pulling the stove out disturbs the cord.

Pulling out a stove is a fairly major operation, I would take the opportunity to completely clean under it and update whatever I could. 

Changing the receptacle would be a decision based on it's current condition (one crack -> replace; any green copper -> replace) and the state of the wires. Open your breaker panel and check the stove wires (they'll be the biggest ones). Still soft and flexible? New receptacle.

A stove is your house's biggest power consumer. Maybe you don't mind a 40 year old cord handling all that power; how do you feel about a 60 year old cord? That's the old cord in another 20 years. If the original cord was recycled itself, it is now 60 years old and will be 80 when you retire.