If we can't responsibly keep track of the waste we're producing then we shouldn't produce it. I'm pro-nuclear, and I think we can do it, but we need to be the kind of civilization that can plan beyond the next quarter first.
[1] https://oceanliteracy.unesco.org/ocean-exploration/, https://oceanservice.noaa.gov/facts/exploration.html
Now, seriously, screwing with ecosystems we know nothing about is a very bad idea, even if for no other reason than we being unable to study them after we turn them into radioactive deserts.
Dig into the rising costs, and you find root causes like 3 mile island showing the industry it needed to increase maintenance spending. It wasn’t some arbitrary overreaction but simply the damage accumulated enough to cost a billion+ dollar asset. Thus much of that “increased” spending is simply asset preservation.
No wonder that dumping nuclear waste to river and oceans is cheaper than having to safely store it for at least a couple of centuries.