Not everyone can get insurance (or get it at an affordable rate).
People who live in areas which are subject to flooding often find that they can't insure their house contents against anything (not just flooding), so they're left with no cover when their properties are burgled.
People who've got unspent criminal convictions (or who live in a house where another resident has unspent criminal convictions) often find it hard to get household insurance at an affordable rate (if they're offered any insurance cover at all). So a perfectly law-abiding householder, whose teenage son (still living at home) gets into some fairly minor trouble with the police, might be left with no insurance cover.
People living on benefits (despite what the Daily Mail might say) often struggle to meet basic bills. I've taught kids (back in the 80s) whose parents couldn't afford to send them to school with a pen, simply because they hadn't got 10p to pay for one. Such families have no chance of affording insurance cover.
Indeed, many people living on low incomes (even if they're not on benefits) can't afford household insurance. That's why I've not got any!