"Compared to these, the effects you described are negligible" is also a positive claim, and I did at least as much work sketching out why I believe my claim as you did sketching out why you believe yours.
Your claim is the opposite. You can prove it by showing that employer provided insurance started growing before the given government involvement.
I doubt that evidence exists.
My claim is that, once established, the resulting equilibrium is economically stable. Your claim, as I understand it, is that it's not.
Given that the price controls that we agree created the current status quo were replaced by significantly less coercive tax incentives decades ago and to the best of my knowledge the industry hasn't attempted to realign away from employer-provided insurance since then, I don't see a reason to privilege your hypothesis over mine.