You are comparing apples with oranges... hydrogen fuel is used (with oxygen) because it is light and accelerates fast in the combustion reaction.
With ion propulsion it is different as it uses magnetism for acceleration... any material can be used... just strip off an electronic and it has an electric charge and can be manipulated easily by magnetic field.
Xenon was chosen because of its very high performance, but nitrogen is orders of magnitude cheaper and much more abundant... it is a bit like airships... hydrogen is cheaper and offers better performance but Helium was safer but expensive.
Old airships used Helium for safety but new airships can use hydrogen fuel cells, and lots of fire retardant technologies to minimise the risk of fire allowing much cheaper operations.
Nuclear thermal rocket has to use hydrogen, if it using helium ( second best candidate in the periodic table ) then the performance of it will be inferior compared to the chemical rockets.
A nuclear ramjet will use the gases the aircraft or missile the ramjet propels is flying through...
I don't think that the reactor has that much margin to locally shut it down and still operating.
I have never heard of any nuclear reactor that "drops cores" except in the Movies like Star Trek.
You need to have the reactor in an inactive state otherwise its engine will always be running... how would you store them?
I would expect in operation when the solid rocket booster engine fires and launches the missile control rods will be raised to expose the fuel rods and the nuclear reaction will rapidly generate heat, which is used to propel the missile... if the reactor overheats the control rods can be dropped down to stop the reaction... the engine wont go cold but will stop heating up and with the airflow drawing heat from the reactor it should stop overheating and start to cool down to a safer temperature...
In fact you could modify the reactor so that control rods remain in place and when the target is reached the missile climbs to 5,000m altitude and drops its warhead or 4-5 warheads over the targets and then the extra control rods can be raised to super heat the engine and melt it down so the missile crashes with a melted down reactor deep inside enemy territory somewhere as a bonus little present...
Operating at higher altitude might require more heat from the reactor so that extra heat potential could make it able to fly faster at higher altitudes too.
Ok, so same theory, .
Ion engine : it requiring only electrical source to operate, it can be reactor, solar cell, battery, RTG, steam turbine.
The reaction mass theoretically can be anything, but in practice it has many design considerations, including but not limited to be easy to storage, don't damage the cathode/anode, be preferably gas / liquid during the operations condition of the spacecraft without complex heating equipment.
Based on those requirements it needs to be noble gas, with high mass .So , they using the xenon.
Nuclear thermal ROCKET engine:
It can work only with hydrogen. Everything else will be worst than a simple chemical rocket.
However this engines can use the hydrogen as moderator in the reactor, so the nuclear reaction would be proportional to the density of hydrogen flowing through the core.
Means it is a self regulating engine.
If the engine fail, then it just impact the ground in one piece ( depending on the design).
Nuclear ramjet engine:
So, the air has no moderating capability. It means that if the flow in the engine decreasing ( even locally) then the reactor core ( the air flow thought of it) will overheat, melt and the derbies/vapour of the reactor core will go out from the engine with the air flow.
Means this engine has higher chance to fail than the hydrogen thermal rocket one, and if fail then it will not just simply impact the ground in one piece, but it will disperse the reactor core over a huge area prior of impact.
So, it is not so easy to test.
Remark: all low earth orbit nuclear reactor system had core evacuation/ejection mechanism, to eject the reactor core to a safe parking orbit.
It is a basic feature : )