The last major breakthrough in quantum physics led to transistors, microchips, solar electric panels, LEDs and a great many other things you probably imagine were the work of some hard-headed engineer working for some corporate research lab. And nobody knew in advance that any of this would come from what looked like blue-sky pure research (or as you might have put it, throwing money down the drain.)
Will CERN produce some breakthrough that will save the world (e.g. a practical recipe for microfusion)? Probably not, but the one thing that's certain is that if we don't do the research we'll never know.