First, these are lower stages, not upper stages. If an upper stage fails to reach high enough orbit, it can re-enter practically anywhere (depending on the intended orbit's inclination, of course).
Second, when conventional upper stage re-enters, it just disintegrates and burns up. The resulting debris is usually pretty harmless. If an NTR stage re-entered, it would either disintegrate too, releasing tens of kilograms of really nasty stuff, or it would fall down in one piece. If it hit a populated area, it could cause both damage and contamination.
Even though conventional stage causing some damage would be bad, the same kind of mishap involving a hot NTR stage would be disastrous. And I mean truly DISASTROUS. It would probably lead to some kind of intensified anti-nuclear hysteria followed by a ban on NTR technology.
For these reasons, I don't think using NTRs inside Earth's atmosphere and below stable LEO orbits would be wise.
Reenter almost anywhere, yes, but it is important to note that most of the Earth's surface is sparsely populated, desert, steppe, ocean, etc.
The NTR engine components and fuel elements, specifically, would be designed to operate
within a rocket engine, where the conditions could be considered similar to reentry conditions... I don't think there is much of a problem with major radioactivity dispersion.
This kind of thing hitting a populated area is a real worst case scenario, it is one you already run with any kind of debris in LEO, and one that definitely doesn't need to be nuclear to be a disaster.
I'd be more worried by a PR disaster, to be honest, all of this talk of nuclear disasters and whatnot is overdone, nuclear technology is not engineered by chimps in hard-hats.
Furthermore the whole point is that you wouldn't use it on an ordinary expendable stage that you
just leave in LEO to randomly reenter, that is bad foresight blindness.
You know politics. You can push something through just barely, only to see the whole scheme collapse when something goes wrong.
And you're saying that a nuclear rocket has an intent to destroy itself?
If the public is smart enough to fully understand the nature of this technology, they wouldn't throw such a fit when they hear news of, say, "minor radioactivity release over the Pacific".
Try telling that to the average Joe. "Don't worry, when our nuke rockets fail, they just blow up"
The rockets blow up, the components that contain radioactive materials do not. Simple.
That's how you engineer things, especially things like this. You engineer it not to go wrong, you engineer it to go wrong safely when it does go wrong, and you engineer the impact to be as minimal as possible if it goes wrong in a way that you didn't forsee or compensate for.
NTRs have never been tested in space (as far as I know), so common sense tells me there are dozens of things that will go wrong once we start testing them there.
I don't know anything that makes engine testing in space automatically more dangerous to the point that engines start blowing up as often as the pyrotechnics in a 4th of July fireworks display, unless, maybe... Alien Space Bats. I dunno...
I have a hunch that the internal forces on the rocket engine are far worse than anything the environment of space can unleash on it, at least on the short term.
Depends on the failure. If you planned an NTR upper stage intended to boost your rocket's LEO/whatever capability, you'd have to keep it relatively light, which means you wouldn't be able to provide it with all the shielding and other stuff to survive all possible modes of re-entry in one piece. I don't know, I am just guessing here.
It's built to survive in very adverse conditions already, so reentry would be relatively easy to survive. In addition such heavy, monolithic parts tend to be the ones that survive, obviously it'd be built to survive more easily than your run of the mill engine, but it shouldn't be very problematic considering that an engine is already quite a (relatively) durable component.
In any case, the public wouldn't care anyway. For the average Joe, nuclear = scary black magic. The activists are eagerly jumping at every opportunity to demonize nuclear energy still more and they'd certainly use any NTR accident to their advantage. We'd better deny them that chance.
So... if you can't use nuclear energy because an accident might demonize it in the eyes of activists, what's the point about worrying about using it at all?
Again, you need to develop a feel for how the "uneducated masses" think. "They're shooting nuclear reactors full of DEATH down to Earth in giant fireballs. OMG we're all gonna die, somebody stop this!"
That is when they remain uneducated. The whole point is to educate the public (through propaganda about nuclear technology :shifty

to a point where they have a rational outlook. As Urwumpe says, the average Joe deserves more credit than one might give him.
I didn't say there would be no maintenance. But given the fact this rocket is unmanned, doesn't use solid rocket boosters (that need to be recovered from the ocean, disassembled, refilled with propellant, furnished with new parachutes, and gods know what else) doesn't use (expendable) external tank that needs to be attached to the stack, the overall recurring costs should be much lower compared to STS. Especially if you avoided building a standing army of thousands of engineers and bureaucrat running the show.
If you had enough orders and decent enough launch rate, it could still make enough money to make economic sense.
I get what you are saying exactly, but the problem is that the maintainance and refurbishment
costs more than building a new external tank, and reassembling, refueling and repacking those solid rocket boosters.
For example the boosters have four engines each, and you have to refurbish all of them after each flight. And if we look at the SSMEs, that is not easy. In addition to that you have to refurbish the engines on the main booster, and it's thermal protection system, as well as the myriad of other systems.
In the end you
need the workforce of thousands, because there's so much work needed getting the vehicle to fly.
Reusability doesn't automatically make things cheaper. There is a threshold beyond which it's cheaper just to build a new rocket, and the shuttle is a good example of it.
No, sorry, the sea isn't a giant waste. That's the most precious thing we have and that Ocean of liquid water is unique in the solar system.
The most precious thing we have? Very precious maybe, but that statement disregards a lot of other important (or even more important) things.
Either way, the point is, the oceans are
big. Most of the seafloor is a mud covered ecological desert shrouded in eternal darkness from the kilometers of water above.
A few rockets dumping some residual kerosene should not be a problem, when compared to the amount of hydrocarbons that are leaked into the oceans each year due to manmade activities, and even
natural processes.