Regardless of whether risk can be reduced for all parties or even estimated correctly, it can still be reduced for one party by being transferred to another who is willing to accept the much higher chance of loss, even a loss that effectively means accepting a negative expected return -- gambling.  If this wasn't the case, it would be mathematically impossible for casinos to remain profitable, would it not?

In such cases, yes, the wealth of the gambler must be high enough to be able to cover the event of loss without being catastrophic to the system, and that was not the case at the beginning of the credit crisis. In other words, the CDO market in 2007 didn't have an enforcer capable of kneecapping AIG and its investors to cover the losses, due to poor oversight by financial authorities.  But that doesn't mean it can't work if such oversight and enforcement exists.

However, keep in mind that "exotic" just means customized, over the counter contract specific to a particular case. You often need them for the same reason that many other kinds of insurance contracts are specific to individual cases.  

Credit risks are really only weakly correlated.  Even in the worst of the current credit crisis, most loans are not being defaulted. Therefore they are easily insurable.

Last point I agree completely. This is the principal-agent problem, and it is aggravated by the fact, alluded to by Migeru, above, that lenders usually have better information than insurers and borrowers in these cases.

However, default derivatives, CDOs, are really only a very small part of the derivatives being done by financial organizations, and even less so today. Most of them are interest-rate derivatives unrelated to default, where risk is traded for interest payments and these have none of the problems you associate with default speculation.