Mandating insurance forces premiums _down_ because the pool of insured people becomes much bigger.
Thats not how it works.
Increasing the number of insured people is meaningless to the premiums needed unless the amount of risk associated with the "new" policies is as-a-matter-of-fact less than the amount of risk associated with the "old" policies. Now if thats true AND both "new" and "old" are in the same pool, only THEN would the cost of policies change.
What you have done is taken an argument from another situation (perhaps the liberal justification for getting everyone on health insurance), and then misapplied it to this one. The reason you misapplied it is because you never understood it to begin with.
Whats worse is even if you understood the argument, you probably still wouldnt understand the injustice of it (which is that less risky people are forced to subsidize more risky people if you force them into the same risk pool.)
Yeah.. I know.. understanding the money is hard, which is why you don't.