ETOPS seems to have done pretty well. As far as I know, no ETOPS-certified twinjets have been lost due to both engines failing. There are a couple cases of the jet running out of fuel (the famous Gimli glider and Air Transat Flight 236), but that is going to be bad no matter how many engines you have. There are cases of airplanes flying into volcanic ash clouds and losing all engines; but more engines doesn't help you if the air around the plane kills engines. There are some poorly-engineered planes with 3 engines that have had a single-engine failure bring down the entire plane (United Airlines Flight 232).

ETOPS is not just some rubber stamp for a particular model of airplane that manufacturers self-certify (hello, 737 MAX debacle), but rather a process applied to (airframe, engine, airline). You have to service particular engines to particular standards to be allowed to fly ETOPS, and it depends on the airline. I could go to the store, buy a 777 and hire 4 ATPs and fly a 777... but I wouldn't be allowed to fly it ETOPS, for example.

All in all, the program seems massively successful to me. It saves fuel, which means cheaper flights and less CO2 being generated. That's a good thing. The main downside seems to be medical emergencies; I remember some stories about the aircraft that flew EWR-SIN... it has some special corpse compartments to stash away the inevitable deaths that occurred 9 hours away from an airport. (It had 4 engines, but engines don't perform heart surgery on passengers.)

The reality is that engines are pretty reliable. 2 is the right number.