Your position paraphrased:
‘Tax deductions for health insurance would cause insurance costs to go down.’
Thus we can conclude from that that if we remove existing deductions then prices would go UP!
Call your realtor and ask them what would happen if the deductions for home loans was removed.
ECON 101. If you really cared.
It is called the law of marginal utility.
Putting in tax deductions for health insurance would allow people to buy insurance who couldn't normally afford it and keep the Government out of the business.