I don't buy that. Sure, that's true: there's billions of tons of uranium in the ocean and nothing bad happens—but it's *also* true that we added just a few thousand tons of mercury, and there's already fish that are hazardous to human health as a result. There's large chemical differences, in how different things are absorbed by microbes, and bioaccumulate in sea life; it's not an automatic given that everything's as comparatively safe as soluble uranium. (And don't forget: spent nuclear fuel isn't one element—it's about half of the entire periodic table. Many of those transuranics are barely researched, chemically).
This is a question that would need to be extensively researched, before committing to something that's irreversible on a geological timescale. Handwaving arguments aren't enough, for something this important, this consequential.
(There's actually rather a lot of spent nuclear reactors littering the ocean floor, so opportunities to research this question are available right now—if any scientists could be bothered).