But the reason why companies were so happy to lend so much money was caused by a belief, which turned out to be false, that loans securized into CDOs and such papers, frequently rated well, are safe and risk is properly managed.

The betting merely caused a spread of the risk between all market participants, making it systematic risk. Also, the betting was not properly managed because market partipicants weren't able to understand the risk.

Also, one might say that the reason why companies started securization and, then, betting on the papers are low interest rates, but, please, let's don't dig into the whole Fed discussion.

The betting didn't just spread the risk, it magnified it.

For every dollar the banks lost on bad loans they probably lost 30 dollars of bets on those loans. No one even knows the exact number because the market is completely unregulated.

And the reason why banks, and not only banks, lost so much on the papers is because the loans were basically worthless. Banks knew that loans were worthless but the paper's ratings created a different impression, boosting the loans.

The spread part is very important. If there were no betting, selling and reselling of the papers, then only bad lenders would collapse.