It does sound horribly risky. I suppose in theory you could mandate basic levels of insurance, a bit like mandatory car insurance, but you'd probably end up with a costly, patchy mess like the US health system.
Mandatory car insurance is usually liability insurance, that is comparatively easy to regulate while leaving other things like pricing to the market. Liability for a car accident also sounds somewhat more manageable than liability for a fire on your house spreading to your neighbors' - I think you're right that requiring insurance for that would be overly messy.
How many people drive around without insurance right now though and even people who don't have driver's license. It just isn't practical to think people will do it, especially when times get tough. If I'm choosing which bill to pay, I'll take the water bill over the insurance bill