With regard to your first one, under my recommended alternative to ESHI, universal catastrophic coverage, everyone would pay their fair share so a good part of the inequality in coverage would disappear, except to the extent wealthy people paid for premium service out of their own pockets. You can find my thoughts on that here.
Your second question is about work incentives. The effect of health care coverage on work incentives is the same as for other social benefits, including specialized benefits like Medicaid or broader benefits such as universal basic income. You can find my thoughts about work incentives here and here.