Is it bad to take aleve (naproxen) everyday for headaches?

Symptoms vs Cure: Not in general. But wouldn't it be a better approach to find out the cause of the headaches and treat that rather than just treating the symptoms of the headache?

Usually not: Taking one alive daily if otherwise health should not be a problem(chronic use of any anti inflammatory drug could cause liver disease or kidney problems). The greater concern is why you get daily headaches. If this is persistent you should seek medical evaluation.