If you want to talk theory then you want a liquid with a super high specific heat or heat capacity that is also liquid at common temperatures to avoid having to deal with internal pressure.
When talking about closed loops you always need a radiator or some device to remove heat from the system.
LN2 in the conventional sense does not need a radiator due to it achieving its heat removing properties by evaporation.
https://en.wikipedia.org/wiki/Heat_capacity#Table_of_specific_heat_capacities
https://www.aiche.org/resources/publications/cep/2015/september/cool-down-liquid-nitrogen
Specific heat is the ability of a material to store thermal energy
Water: 4.18
Ammonia: 4.7
Hydrogen gas: 14.3
Liquid Nitrogen: 1.08 at 1 atmospheric pressure
Technically Ammonia has a higher heat capacity than water, but due to ammonia boiling at −33.34 °C you would need to keep the temperature of your closed loop below that which is achievable.
The issue with ammonia comes with ammonia's acidity slowly corroding most metals along with its toxicity to most forms of life.
Depending on how much ammonia is in your loop it could be highly hazardous if your house were to lose power and your loop was unable to sustain the pressure of all the ammonia flashing to gas.
Hence why consumers don't use ammonia for cooling.
(Industry might for some obscure purpose, but other chemicals are much safer)
As for hydrogen:
It requires a massive amount of energy to make it a liquid, -252°C or 21 kelvin.
This means super insulting your pipes as well.
We can't have room temperature air causing convection/conduction to occur against our 21 kelvin pipes.
On top of that any leaks you might have require the evacuation of the neighborhood.
I couldn't find the specific heat of liquid hydrogen, but it's best to not try to find it lol.
Now we full circle back to liquid nitrogen;
Cooling nitrogen to its liquid state, -196 °C or 63 Kelvin, requires a lot of energy.
We again need to super insulate the pipes against heat transfer.
Liquid nitrogen also has a specific heat 1/4 that of water.
This means that it will heat up much faster than water causing your radiator to work even harder to cool it back down to a liquid state.
You can make a closed liquid nitrogen loop with a highly specialized radiator such as one implementing a peltier heat pump, but the thermal properties of liquid nitrogen make it highly inefficient.
This makes liquid nitrogen only suitable for short term record-breaking through its heat transfer through evaporation
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