Hey, that's the most sensible thing I've heard all day! I should try that myself.
"Before I sign up, could you please tell me what this health insurance policy's premiums were last year? Yes, I understand that you'd like 25% more this year, but I think we should all agree it's more reasonable to expect an increase of 10% at most. Now, let's talk about my expectation for you to go the extra mile when there's additional medical work to be covered -- without additional pay, of course."
Apologies to those readers in first- and second-world countries where this "signing up for health insurance coverage" analogy is sensibly unintelligible.