The difference is that insurance is not about the expected return at all - it's about managing risk. The "payout" from insurance is tied to events that can happen whether or not you have insurance, and which would ruin you financially without it.
The expected payout from insurance is only relevant when the above does not hold, i.e. you have enough liquid funds to cover the loss against which you're insured. A good example are non-health-related travel insurances (e.g. against cancellation expenses or baggage loss). Your argument is correct in these cases - these insurances are a net loss and cover a risk that you could simply bear. So you should not buy them.
Exactly. If risk is defined as financial uncertainty, then lottery tickets and insurance are in fact complete opposites with regard to managing risk. Insurance is designed to minimize financial uncertainty and lottery tickets (gambling) to increase it.
Indeed. Also, most people are risk averse, so they are happy to purchase insurance with an EV (expected value) equal to less than the premium simply to avoid the gamble.
The expected payout from insurance is only relevant when the above does not hold, i.e. you have enough liquid funds to cover the loss against which you're insured. A good example are non-health-related travel insurances (e.g. against cancellation expenses or baggage loss). Your argument is correct in these cases - these insurances are a net loss and cover a risk that you could simply bear. So you should not buy them.