Secondly most of the countries involved in this are US allies, and in fact US scientific institutions play an essential role in it. Why wouldn't they? This sort of thing is what us marine scientific research organisations exist for.
Thirdly US mining companies could stand to make billions off the back of this sort of data. Why pass that up, or drive such benefits abroad?
Finally, imposing such a ban would be tantamount to the US declaring unilateral sovereignty over all of the Earth's oceans and their contents. I know the current administration doesn't seem too bothered about snubbing it's closes allies, but even if the US wanted to do this, they couldn't. They don't have anywhere close to the assets to monitor and interdict all the Earth's oceans. They certainly don't have the capacity to do that and also carry out the security and defence missions their naval and air assets are already assigned to.
So what part of their current security commitments do you think the US would be willing to give up to try and enforce such a ban? Do you think alienating all their allies would make it easier or harder to carry out those existing commitments?
If wishes were fishes....
And while that's a very long sentence, this is just a "public" version of the same.
And I would assume they would protect those assets against other submersible devices
Historically, the country which claimed international jurisdiction over the sea was the UK.
Some kind of secret base on the abyssal plain?
The cost for such a thing would be astronomical, with no appreciable benefit.
They don't own the oceans.
Iraq and Afghanistan, for starters. If the US doesn't allow something and you do it anyway, you tend to come up with a nasty case of Dead.
Arrogance or not the force that the US government can exert anywhere in the world at any time they want is real.
I'd be willing to wager we have some under water assets that we don't necessarily want to be discovered.