So far as I know there is nothing in physics that would prevent such a thing - I think the issue is whatever tensioning device you use (unsure if piezo is the way to go or something else), each unit would be responsible for a relatively small number of atoms (maybe ~10, maybe ~10^6, hard to even guess) which means these devices are probably going to require atomically-precise manufacturing. And any practical application of superconductor material is going to have 10^23 atoms or more. So now you need 10^17 atomically-precise tensioning devices… it’s much easier to let e.g. magnetic fields do this work.
I think the “tension axis” is more likely to be fruitful in a different way, where we find some structure e.g. a crystalline formation that happens to hold atoms apart with just the right amount of tension. But this is all very speculative - the “tension axis” is just a random thought I had while reading the article!