What you're getting at is that there is a reason people buy insurance anyway -- the peace of mind that that won't happen to you, as I mentioned. Because a million dollars in claims money even if you have to multiply it by the only 2% probability of that happening is worth more to you than the $20,000 in guaranteed premiums you'll have to pay over your life, because if the claim actually happens you need the money more. The value of the same dollar is higher to you then, which you can predict from the beginning and account for.
But that value still has to be balanced against the losses to administration and fraud, and balanced against what you need the money for today. If losing $100/month to premiums causes you to starve now, it doesn't matter that there is a 2% chance that you starve in ten years from now. If the majority of insurance claims are fraudulent, the higher value of the money in case you have a legitimate claim may no longer exceed the losses from buying the insurance.
It's possible that buying insurance makes sense. It's possible that it doesn't. But people should be able to make that choice for themselves instead of having it imposed on them.
It is an externality. Maybe you don't mind having the streets of your town full of homeless people, but I do. In fact, I mind it very much. When someone ends up on the street, that makes my life less pleasant even though I'm not the one who was uninsured.
The person taking the brunt of the hardship is clearly the person suffering it and not the person with the misfortune of having to observe them, and they also have the best incentive to take steps to prevent that from happening. Forcing choices on them doesn't fix it. Maybe it makes it so you don't have to look at them, but if the net result is sufficiently worse that they wouldn't have chosen it given the choice, you're not actually helping them, you're just making the suffering less visible.
Of course that is true. That doesn't mean that the cost imposed on others is zero.
It's never zero. But you're making it out to be a significant cost relative to the effect on the person making the decision. Having a way to internalize the cost of others' displeasure at being aware of their possible misfortune wouldn't materially affect their decision one way or the other, because it's so much smaller a factor than the possible misfortune to begin with.
But you're making a fine argument for charity. If a thousand people don't want to see a person go homeless, it doesn't take much from each of them to make it so they don't have to.
And if 1000 is not a big enough number to make you think twice, then make it 10,000. Or 100,000. (The number of homeless in the U.S. is considerably larger than that BTW.)
You're comparing the entire US homeless population to one person. The actual ratio is less than one in five hundred.
That doesn't make the cost of feeding people who can't afford food any less of an externality.
Only if you ignore externalities, like uninsured permanently disabled people begging on the streets or starving to death.