I don't know the level of your knowledge of electrical principles, and in particular of the practical aspects of superconducting cables, so please forgive me if I seem to deal with ideas that either are too simple or too complicated.
Firstly, bear in mind that there are no true infinities in physics. When ever you deal with anything of the kind, then a lot of assumptions start going wrong when the scale of any parameter becomes excessive.
For example, electric current is a simple thing. Electrons move in a piece of wire or whatever it might be (actually for most purposes the electrons hardly move; it is their waves that propagate through the conductor at the speed of light in the conductor). You could hardly get simpler than that could you? Stick to the simple things and you will be all right!
Except...
It isn't really nearly so simple in practice. It may look so simple at low voltages and amperages, but we have to remember that current carriers such as electrons have charges. These charges must be on average the same, otherwise there would be no net electric current. But like charges repel, and they don't stop repelling each other just because they happen to be in a cable. One consequence is that as your voltage and current increase, you wind up with hardly any current inside the conductor and everything moving in the skin of the conductor. You will very likely by now have heard of the "skin effect".
Another thing is that as soon as you move an electric charge such as an electron, you create a magnetic field. Right?
Did anyone explain to you the difference between hard and soft superconductors? When I was a boy only soft superconductors were known. They would only work very, very close to absolute zero. It was quite a thrill when some workers described niobium alloys that could remain superconductive at liquid hydrogen temperatures. Even then, it seemed unlikely that superconduction ever would be practical for any purposes. It was all very well to have effectively zero resistance for minute currents, but even a slight magnetic field would destroy the superconductivity, and any useful current created a magnetic field that would quench the superconductivity immediately.
It was something of a red letter day when the first "hard" superconductors were discovered and superconducting solenoids became possible.
Even then, there were limits to practical field strengths, electric or magnetic, and of course users and research workers always wanted more than was available. When even the hardest superconductors were used, they tended to be used at the limits of their capabilities. Surprised?
One thing that happened regularly was that in any realistic high current, high magnetic strength device, there would be occasional loss, "quenching" of superconductivity, and the result commonly was explosive. Various tricks were tried, such as braiding the superconductive material with copper that could act as a transient buffer where superconductivity failed, or using thicker superconductors in the hope that some parts of the cross-section would remain superconducting at all times, or using multiple-stand superconducting cables.
I am sure that you can see where this is going!
By increasing the conducting cross section one not only improves more than just the current carrying capacity as might happen with a normal conducting strand, but increases the current that can be carried without the skin effect magnetic penalties I have mentioned. Unfortunately, as always with superconductors, there still are more complications. The currents in neighbouring strands interfere with each other, and the longer the strands the greater the interference. For multi-strand cables to work, it becomes necessary to cross-link them at intervals as short as possible, but there are complications to cross-linking them too. For example whatever soldering material you use is likely to affect the superconductive metal as well.
I hope that this will give you some insight into some of the reasons that not everything is as simple as it seems, but at the moment I am too sleepy to talk sense, so if I have left you with any doubts or confusion, feel welcome to let us know.
Cheers,
Jon
