Why hasn't massive derivatives exposures at banks already led to disaster?
While gross notional exposures are huge, net exposures at the banks are much smaller, on the order of 0.1 percent of gross exposures. Since most financial risk (but perhaps not operational risk) is proportional to net exposures this is a more sensible measure of total derivative risk at the banks. Since net exposures at the 6 banks with the largest derivative exposures circa 2014 were on the order of \$300 billion while their total assets were more than \$10 trillion, we may not have seen a disaster because the actual risk is appropriate to the scale of their broader operations. 

Here is an example of how this works. At time 0 a bank does derivative trade with notional of 100 with A and collects the offer (or ask) price. That is, the bank sells the derivative to someone who wants to buy it. At time 1 a bank does derivative trade with B with notional of 100 and collects the bid price. That is, they buy the derivative from someone who wants to sell it. Total (gross) derivative exposure is 200, two derivative contracts each with an exposure of 100. However, net exposure is zero, and the bank keeps the spread as profit for its trouble. There is likely some remaining risk in the form of operations and credit risk, but this is what the spread and initial and variation margin are for.