Biological systems supposedly operate at about one order of magnitude above the Landauer limit [0], i.e this is completely practical and has been happening before we even made computers... we probably wouldn't exist without being this efficient, imagine how much energy our cells would need to consume and emit as heat if it were similar to a CPU of today!
You could absolutely use superconductors for all the connecting wires, and with a little engineering it might also be good for conducting heat away from the chip die as part of the larger CPU package… it wouldn’t be a good interface material (pins for connecting to the motherboard) as you want oxidisation resistance and a level of ductility and malleability to help with making a very good electrical connection between the surfaces when they are mechanically pressed together. But overall it will have some uses, it’s just not an immediately applicable technology for the silicon chips themselves… lots of potential in circuit designs and I’m sure if someone invented a way to lay this material onto a PCB as easily as we can print copper traces on them today that inventor would get pretty rich… it’s just not likely to make much of a change to the silicon chip die itself due to the need for semiconductors to do the transistor switching …
Of course someone might have invented a superconducting transistor that I haven’t heard of and if that’s the case disregard most of what I’ve just written haha.
Turns out that some research groups have already built superconducting CPU, albeit tiny ones.
Considering how much faster super conductor logic circuits have been demonstrated to be driven [0] it might be worth the trade even with a higher fundamental limit on feature size.
A super conducting chip with far less logic could easily beat CMOS in: (1) Power performance (2) Single threaded performance (where CMOS has stalled) - but interestingly it could still compete in total throughput if the raw frequency is high enough. i.e even though there may be far less logic available compared to the latest and greatest CMOS lithography techniques - if it runs so much faster, less or simpler cores can potentially match or beat the throughput of the more parallel and specialised but slow logic available in CMOS dies.
In short, it could be like taking a step back in time to the simpler, smaller CPU days, but a huge step forward in fundamental frequency. That actually sounds like a nice trade regardless, CPUs are so insanely complex these days.
</armchair physics>
[0] https://spectrum.ieee.org/superconductor-logic-goes-lowpower
I work in research, so I understand that it is very important to keep in mind the limits imposed by nature itself. Heck, I had more than one argument with idiot bosses who wanted to break the laws of physics or maths...