Actually risk is lowered by the removal of insurance. What insurance does is disseminate the risk, not reduce it. People will undertake risky projects if they can be insured because the risk of failure to them is lessened.
Thus the problem with mortgage backed securities and credit default swaps. People kept doing risky things because (1) they were highly profitable and (2) they could transfer much of the risk to other people and still make a nice profit.
Mortgage originators would not have made loans to people with no money down and no income check if they were depending on those people to pay them back. But they knew they could sell the mortgage as soon as it closed and collect their origination fee. Now it's someone else's problem. The person who bought the mortgage to securitize wouldn't have done so if they couldn't sell the security. And the hedge funds and banks that bought the security wouldn't have done so if the security didn't have a AAA rating. And the security wouldn't have had a AAA rating if they hadn't been insured by the world's largest insurance company, AIG. Thus the whole risky chain would have not been possible without AIG's insurance: essentially, mortgage lenders would have been forced to lend money only to people who they thought would be able to pay them back.
So once again, insurance causes an overall increase in risk-taking: it allows people to engage in risky behavior that they would avoid if they had no insurance. Which is not usually a bad thing. Risk leads to innovation and advancement.
There's something like an equivocation with the word "risk" going on here. You have to be clear about who bears what responsibility. From the perspective of someone engaging in a transaction, paying for insurance limits your potential losses, or risk. But insurance can also lead you to take more chances, or risk.
Those are two separate concepts. Here you're discussing the idea of taking chances beyond what is reasonable. I was discussing the idea of limiting losses. Ideally (or practically for the most part) no insurer would underwrite extraordinary chance. But as we know, the financial industry engaged in wide-spread fraud.
One interesting thing they would do is package a risky mortgage with other financial instruments like car loans or credit card debt. You pool it all together and the odds that
some of it will be payed back is fairly high. This is how they finagled those AAA ratings. Then it's relatively easy to get insurance when you have a AAA rating, then the leveraging...etc.
And the basis for handing out those sub-prime mortgages was that housing prices would raise infinitely. Thus, even if a client couldn't keep up with payments, you could always refinance. This was a silly gamble that had little to do with the concept of insurance. If it were simply the case that they gave houses to people who couldn't pay (another canard as the leading cause of foreclosure is health care costs--meaning many of the people could initially pay, but something intervened), then no one would have allowed them to leverage against the initial mortgage. There was a bizarre adherence to the idea of infinite refinancing.
But the presence of insurance itself
shouldn't cause imprudent behavior because those underwriters wouldn't offer coverage for something so uncertain. There are plenty of things that are too risky to be insured, and the weird financial schemes should have been among them. But all of that fraud allowed the insurers and risk takers to essentially be complicit in a plot to create money.