Your reasoning is far from sound. If it were economical to separate the highly radioactive material from radioactive waste we would be doing that.
There are few more corrosive environments on earth than in the sea. The dry storage casks you mention are just that, "dry" storage, not "at the bottom of the ocean" storage.
You can "monitor" the area all you want. You can't do anything about ships in international waters.
The main problem is that if there were easy solutions, we would be using them. You might as well have suggested that we shoot the waste into the sun.
The good news is that we will be making less and less nuclear waste as the reactors are shut down. In 30 years there will be very few commercial reactors remaining in operation in the US anyway. The costs don't permit it even when you don't count the cost of dealing with the waste. Renewable energy has already crossed the threshold of being cheaper to use than existing installations of fossil fuel. Since nuclear tends to be more expensive than even fossil fuel electrical generation, why would anyone want to build new ones. Every current nuclear project in the US is well behind schedule and well above cost. The three new installations in the EU are horribly so. Funny that nuclear advocates point to France who has something like 80% of their electricity generated by nuclear. It is the French who are designing and putting in these new facilities that are going so horribly wrong.
It's not done because it's cheaper to shove spent fuel into a 'dry' cask than it is to process it. That doesn't mean reprocessing isn't an economic option if you need longer term storage than a dry cask can offer.
And 'dry' refers to the fact it no longer needs active cooling in a spent fuel pool. As I mentioned the ideal solution would be to encase the fuel in glass. Glass doesn't corrode. And dry cask storage is layered. It's designed to be flooded. Be a pretty terrible outdoor storage solution if it wasn't. There wouldn't be any real risk to dumping them into a trench.