The flip side of that is that they aren't contributing much to insurance premiums. At a policy level it may be worth a slight increase in cost if building it into insurance significantly increases the number of people that actually get the shot.
Can we be certain of that? That is, even if the vaccination costs $30 to $40, will the insurance be billed for that amount, or do they get billed something like $300 instead?
I haven't tried to pay for a influenza vaccination out of pocket recently, so I don't know what most places would charge.
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Even so, that's more money that the insurance company is paying out that could just as well be paid for directly everyone who gets the vaccine. If routine care was affordable without having to involve insurance, then insurance premiums wouldn't be as high and the out-of-pocket costs for medical care wouldn't be as high either.