I assume that the issue here is how to prevent losses., i.e. the dissipation of energy. These occur by
1. Electromagnetic radiation
2. Electrical resistance of the wires
3. Lagging response in the core.
No doubt that manufacturer was right that for typical applications the core response is most important. However, superconducting transformers not only eliminate the electrical resistance in the wires but also allow the construction of useful transformers without a core. The core will generate heat as the magnetic domains are constantly flipped in the alternating field of the windings of the transformer, and this is the biggest energy loss in most practical transformers.
To explain, the main role of the magnetic core is to allow much larger magnetic fluxes to be created by a given current. (The core also helps guide the flux between coils in some transformers.) Now the main point of that is to transfer more power to the secondary for a given power to the primary. The primary dissipates power mainly because of its electrical resistance. In a superconducting transformer the primary dissipates no power except for a small electromagnetic radiation term, so near 100% efficiency can be obtained with no core at all. That's a pretty effective way to eliminate core losses.
(published on 10/22/2007)