This is actually real. The problem is that nuclear reactors don't scale in cost or power output very well. Back in the 1960s, we built what was supposed to be a nuclear-powered equivalent to an SSK, i.e. a small, inexpensive hunter-killer that had a scaled down nuclear powerplant. For a brief while she was known as an SSKN but the submarine ended up so like an SSN that's how she was classed. We only built one, the loss in capability wasn't justified by the largely ephemeral cost savings.
Now, since then, one proposal has been to use the RTGs (radioisotope thermoelectric generators) designed for satellites to provide a charging system for an SSK's batteries. RTGs have been used extensively for unmaintained situations that need a relatively low level of output over a long period that cannot be attained by batteries, fuel cells or generators. The first main problem with RTGs is safety which is why they tend to be assigned to unscrewed vehicles. The second main problem is disposal since once pulled from service RTGs require long-term safe storage. Finally, RTGs are expensive. All these things combine to make RTGs an unacceptable source of power for submarines. The long-term operational duration of RTGs doesn't really buy us much since the SSK has to come into port for other reasons at frequent intervals and might as well stock up with fuel for its AIP system then.
There are significant engineering problems with installing RTGs on submarines. These things get seriously hot (they can glow red-hot under some circumstances) and need cooling systems that are unacceptable in a crewed submarine. That also added to the cost of the system and made the cost balance even less favorable. The final issue was that because costs of nuclear reactors do not scale with size and output, for the cost of putting a small reactor in to charge batteries, we might as well put a large one in and drop the rest of the power train.
There are alternative reactor designs coming that might change the cost balance but at that point, some discrete silence is in order.
.
Picking up from the previous post, and submarine operations in shallow water. Operationally we divide oceans into three groups. Blue, Green and Brown. Blue water is oceanic and out there, warships are relatively safe. It's very hard to find them and they are well-placed to avoid and/or destroy attacks. This is where the SSNs roam and where they are at their most capable. Green water is continental shelf waters, shallow and obstructed with bottom debris that makes life very hard. Not impossible though; Ark Royal's 1972 East Coast Rampage was a perfect example of how even a large capital ship close inshore can evade detection while creating havoc. Green water is the realm of the SSK. Finally brown water (so called because of what cities tend to pump into it. There's an old joke that if one is swimming in brown water in the Persian Gulf, one never knows whether the thing nuzzling your leg is a sea-snake or a turd. Or which is the most terrifying) Anyway, brown water is almost impossible for major warships, or minor ones come to that, to operate in. It is the realm of the small coastal submarine.
Another significant thing is that coastal submarines may be cheap and simple but, like sea-snakes, they can have a very nasty bite. The South Korean corvette Cheonan was sunk by one such submarine, a North Korean Yono class boat. This is a copy of a Chinese coastal submarine which was a copy of the Russian M-IV class which was a copy of the German Klasse IID which was a repeat of the WW1 UB design. That's right, the Yono is a copy of a design over 100 years old. The key is, it is old and very simple but (unlike its predecessors) it is armed with lethal, fire-and-forget homing torpedoes. In brown water, that is a deadly combination.
That's why the idea of surface ships taking cover in coastal waters is unrealistic. It's too dangerous. Basically, the further out to sea the ships are, the safer they are.
