Why Not Put Waste in Ocean Trenches?

I hear this one all the time: couldn't we just let the tectonic plates carry our nasty stuff down into the mantle? Quick answer, No, it's too slow, expensive and unsafe. The longer answer is here. Geology isn't fast enough, first, but the human problem is even more problematic. A few decades ago when the space program was new, people often speculated that we could launch nuclear waste into space, maybe into the sun. After a few rocket explosions, nobody says that any more: the cosmic incineration model is infeasible. And the tectonic burial model isn't any better.