Poorer people are more likely to have health risks. They are more stressed, more likely to skimp on preventative care, and don’t eat as healthily as compared to the wealthy.
For the poor to optimize expected utility they should buy insurance because an unfortunate health or natural event could totally ruin them. On average, people lose when they buy insurace (insurance companies are profitable). For the very wealthy it makes the most sense to self-insure. If you have enough money to cover any unexpected (but unlikely) event it makes the most sense to save a bag of gold for a rainy day. Many do this.
Does it make sense to financially penalize people because they have less money? Is the only solution to this inequity a government that will provide universal healthcare and insurance?