Insurance is positive-sum because the value-generating enterprise (the buyer) gets to continue generating value after the unexpected thing happen. The alternatives is that the value creation process just stop. It is only seemingly zero-sum for the point in time when the accident happens and one side has to pay for the other.
Your argument only works for catastrophic insurance.
In practice, people take out insurance even for events that would not put them out of business.
Btw, if you are talking about 'value-generating enterprises', ie businesses as buyers of insurance, then your argument doesn't really work either, or at least not without caveats:
When a business suddenly has a large liability, and it goes bankrupt, all that happens is that the equity owners are wiped out and the creditors take over. The underlying business can and often does continue uninterrupted, and has approximately the same value as a going concern as before.
Also, being able to run as a going concern is of finite value to a business. If your business can take a 51% chance of either doubling in value or alternatively going bust, then that _might_ be a good gamble to take if your shareholders are well-diversified. For example, if index funds are your main shareholders.
Humans need considerable better odds before they consider such a gamble. But people do regularly put their life on the line in return for very finite benefits. Eg every time you leave the house, and drive a car. Or even more stark, any time people conveniently 'forget' to put their seatbelts on.
Events that merely reduce the productivity of your business has the same calculus: insurance helps you get back to speed quickly, and there are values in doing so.
I am not saying that ALL insurances provide values. Like any other kind of trades, you can lose values if you make a bad decision. That does not make insurance inherently zero- or negative-sum.
> When a business suddenly has a large liability, and it goes bankrupt, all that happens is that the equity owners are wiped out and the creditors take over. The underlying business can and often does continue uninterrupted, and has approximately the same value as a going concern as before.
This assumes the original owner brings no value to the business. Even in that case, the disruption itself is harmful, not to mention the assumption that bankrupted business can restructure rather than closing down.
You can close down the business even without a bankruptcy. And you can have a bankruptcy, without closing down.
Closing down the business doesn't necessarily mean very much: all the machines, and workers and real estate and building still exist, whether the business closes or not.
