Yes, there is no "scale" in the SE. The main problem is that you of course also need an relevant Hamiltonian for what you are modeling; preferably one that can be used to solve the problem and for most macroscopic objekt the Hamiltonian is very complicated.
In reality, most people tend to prefer the Heisenberg (or more generally interaction) picture when they model 'simple' macroscopic objects such as superconducting devices for various technical reasons (mainly because it is easier to handle dissipation) but you can always re-write this as a SE
Also, note that solid state qubits are quite large, several square microns (which doesn't sound like much, but you can e.g. easily see them in a decent optical microscope). and they are quite well described by 'simple' SE that can actually be solved.