What do you mean with "inert"? I'm pretty sure most radioactive elements are quite happy to react with other chemicals, like salt water.
Some of the new compounds will be water or fat solvable, and can find it's way in to our food chain. The gasses and particles from the nuclear tests around the world was also fairly localized, and if something was spread, it was diluted in a vast vast amount of air. Still, there was long lasting effects on humans and animals, some of which we are still discovering.
Look at the wiki entry linked above by the OP, most things dumped in the ocean are solid waste.
The look at the environmental impact studies done on the dump sites. They found no or negligible environmental impact. If OP wanted to make an argument against ocean dumping of certain nuclear waste, the wiki articles fails at this, on the contrary, careful reading makes it sound like a really good alternative for certain kinds of waste.
https://www.sciencemag.org/news/2021/04/nuclear-fallout-show...
This is effectively the same mistake as the people back in the day made, thinking that the ocean is so big we cannot impact it.
The half life of many of these materials are very long time and it is extremely ignorant to think that highly radioactive materials won't affect ocean life during that time.
Also, the material may be used as fuel for modern reactors in the future. Now you have dumped a lot of shit that is poision to basically all life which could be used to power society.
Then look at the kind of stuff that they have to bury and store. It's not just the fissile material itself, it's pretty much everything that had to have had contact with it. Wikipedia mentions "steam generators, pumps, lids of reactor pressure vessels" [1] - those seem very reasonable to just dump in the ocean.
I agree that material that can be used as fuel for modern reactors in the future should be kept accessible.
[1] https://en.wikipedia.org/wiki/Ocean_disposal_of_radioactive_...
A firecracker can be life-threatening if you clench your hand around it and let it explode. But that only means you shouldn't let it go off in a tight, enclosed volume, close to something vital.
Look at the wiki article, most of the nuclear materials dumped were solid low level waste. That sounds like it can stay on the bottom of the ocean just fine.
I do not know where most people get this mental image of dumping "barrels of waste" - maybe from movies of something. I will admit this is what I imagined in my mind, but it seems not to conform with reality.