To provide some rough intuition, I might point out that in order for a material to become superconducting, there must be some interaction in the material that allows the electrons to form Cooper pairs, and these interactions are more likely to occur in crystalline systems. In typical BCS superconductors for example, the electrons interact with atomic lattice vibrations (called phonons) to form these pairs. The work being discussed indicates that the relevant interactions are (magnetic) superexchange interactions between electrons are relevant in the cuprates (although I'd say more work is necessary to be sure). In both cases, the structure of the crystal lattice is important for determining how these interactions take place. That said, I'm aware of some amorphous (i.e. non-crystalline) superconductors, although I'm by no means an expert in these.

Another point to consider is that most chemically homogeneous solids are in principle crystalline, although in practice a chunk of matieral may be made of very many tiny crystals stuck together in random orientations.

As for whether nanoscale structure could have a significant effect, that question forms a pretty major part of my current research. The stuff I'm actively working on isn't ready to publish yet, but to repeat the example I mentioned elsewhere in the comments, my colleagues were able to increase the superconducting transition temperature of strontium titanate by almost a factor of 2 by plastic deformation (i.e. squeezing it until we start messing up the structure) [0][1] (full disclosure: I'm one of the authors of this paper). We think this basically occurs by modifying the nanoscale structure in a way that introduces mechanical strain in the crystal, and this strain in turn influences the electronic interactions in such a way as to locally increase the superconducting transition temperature. In a general sense, this is somewhat similar to the fact that in many cases, applying high pressure to many superconductors will increase their transition temperature.

[0] https://www.nature.com/articles/s41563-021-01102-3 [1] https://arxiv.org/abs/2005.00514 (same paper as above, but in a non-peer-reviewed and paywall-free version)