Do you have ANY idea how big the Pacific Ocean is ? It's HALF the planet. A couple of nuclear reactors wouldn't even make it burp.
I don't think the ENTIRE Pacific Ocean would become radioactive, probably a few cubic miles of it. The point is that it would be an exceedingly difficult problem to deal with. At least with Chernobyl you can put up a fence and prevent animals from going in & out. You can dig up the radioactive dirt and put it somewhere. But it's very difficult to put up a fence in the ocean, so all the sea life in the exposed areas would be subjected to high amounts of harmful radiation. All of that is only with the assumption that the radioactive steam didn't send millions of gallons of fallout up into the atmosphere. And then there's the possibility that much of the radioactive water could migrate to some shoreline. And this harmful radiation would have a half life of, what is it, 2500 years? That is truly a terrible downside. Sure, only 1 person died in Ted Kennedy's car, but once that car was pulled out of the water there was no more danger to humanity. There was only the potential for maybe half a dozen deaths in that "accident", but there's a potential for hundreds of thousands of deaths due to radiation sickness and cancer from just one sunken nuclear ship.
On top of that severe downside, it is my belief that once Americans view such a terrible outcome, they would lose stomach for sending more soldiers to die for Taiwan.