This seems like a no-brainer. For healthy and relatively young (31) people like me, my personal benefit from getting the flu shot is in many ways less than the net benefit incurred by other more vulnerable people in the population. There is a huge societal benefit to having as many people get flu shots as possible, whereas my personal benefit is more modest.
As I understand it, co-pays don't directly affect insurance companies' bottom lines all that much. (Instead, they make their profit by denying coverage as often as possible, but that's a separate rant) The main purpose of co-pays is to make it so that the insured has a personal cost as well, with the idea being that they will be less likely to get unnecessary treatments. In other words, it is an attempt to bring the insured's personal cost-benefit tradeoff more in line with the overall cost-benefit.
But for a treatment in which there is a major positive externality, a co-pay is just ridiculous. You're moving the insured's personal cost-benefit tradeoff in the wrong direction.
To be honest, I'm baffled that insurance companies don't voluntarily fix this. Surely, getting all of their insured to get flu shots would reduce their overall costs? But if the insurance companies won't do it, the gov't should. It should not be legal for a health insurance company to charge a co-pay for a flu shot, or for any type of vaccination for that matter.