Second but probably more importantly you are correct that protons and neutrons are strongly bonded as part of a nucleus, what I think you are missing is that hydrogen molecules are essentially free-ranging protons and do not experience nuclear bonds with oxygen molecules as part of water, they are instead electrically bonded. It is not incorrect and even somewhat common to refer to hydrogen as being a proton, because typically it is. Sometimes you'll get heavier hydrogen with neutrons, but mostly you don't. Hydrogen also has a difficult time trapping and keeping electrons, so seeing it as a sort of 'hanger on' proton when its bonded is normal too.
I'm not aware of any thing that we humans use where a proton is the primary charge-carrier. I also won't speculate as to what sort of material properties they would have. If your thesis is 'protons as charge carriers is extremely unusual' then yes you would be correct. The reason that 'most substances conduct electrons' is because metals already conduct charge, which you are probably familiar with as the 'sea of electrons' theory, and semiconductors also use electrons or electron analogues as their charge carrier.
Does that answer your questions/doubts?
according to the article:
> The oxygen atoms form a cubic lattice, but the hydrogen atoms spill free, flowing like a liquid through the rigid cage of oxygens
Hydrogen consists of a nucleus of just one proton.
> I feel [electrical resistance] should be extremely high
electrical resistance measures the opposition to a flow of current, whereas electrical reactance measures the opposition to a change in current.
If you are thinking about momentum, do you mean reactance?
> protons have extremely strong bonds to the nucleus
Protons are chemical shorthand for the H+ atomic ion. They are bound to the fluffy outer electron shells of oxygen atoms in water.
> If so, are there other such substances that conduct electricity with protons?
This is basically how the inside of some fuel cells work (note that there is a counter-flow, which is the "useful electricity" of electrons that travels OUTSIDE the fuel cell, but inside of the fuel cell the electricity flow is via H+)
https://en.wikipedia.org/wiki/Proton-exchange_membrane_fuel_...
If so, are there other such substances that conduct electricity with protons? What is the electrical resistance of such substances? I feel it should be extremely high due to the increased mass of the protons.