I don't follow. If the goal is insurance then why not just have... something more like insurance? Like when you buy insurance for your car or home? We don't let randos buy options on the average Joe's mortgage or car loan and claim it helps price discovery or liquidity, right? Or is it the case that even I can do that and I'm just out of the loop?
To answer your question directly, there are active markets where insurance policies are effectively "traded" like this (reinsurance and retrocession and the Lloyds market). A single policy with sufficient limits absolutely does get syndicated out and bought like this. For smaller policies they get bundled up. But they're professional markets where participants must be regulated because insurance regulation is how we mitigate counterparty credit risk on insurance policies.
But "like insurance" I think was meant as a broader term. Traditional insurance contracts look a bit like options. But forward purchases or sales are also often used as "insurance". The big gain is that purely cash settled contracts (or contracts where cash settlement is possible as a result of sufficient market liquidity existing to allow closing a position before physical settlement) can be used for risk mitigation in other ways which offer much better liquidity and better cost-efficiency in the right markets.
A good real world example is oil price hedging. An airline might want to mitigate the risk that their future cost of jet A-1 goes up. On the other hand, an oil producer might want to mitigate the risk that their future sale price of a particular blend of their crude goes down. Instead of using insurance or entering into bilateral forward contracts, both can trade futures or options on a standardised crude (which neither of them is ever planning to physically deliver or take delivery of[0]). The contract they are trading will not be a perfect hedge for either of them, but it will mitigate their risk significantly. In fact if they are both large enough, bilaterally the liquidity available to them would likely be insufficient to mitigate the same amount of risk.
Having a "single", transparent price also brings some other benefits beyond simple liquidity. For example, it enables several ways to manage counterparty credit risk which would otherwise be unavailable (daily margining, use of central counterparties or clearing, etc).
[0] although the contract might enable an oil producer to make physical delivery of their own blend with a price adjustment
I don't know, but one reason might be history. Modern insurance companies are pretty recent. Before the 1920's, there were mutual-aid societies. Commodities trading is ancient.
But they also do different things:
You need insurance companies for one-off risks. Someone has to go see the house and say, "yep, it burned down." Also, we don't let people bet on other people's houses burning down for good reason.
Other risks are more impersonal, like "what if this company I bought a bond from goes bankrupt" or "what if the price of corn drops in half" or "what if the price of oil doubles." There are lots of people and companies who might want to hedge against those, not just the owner of the property.
