Solving electromagnetic problems using circuit representation

I have a very general question and am looking more for guidance from more experienced engineers than a right answer

Many common circuits with interacting electromagnetic phenomenon are can be solved using circuit representations of the physics (i.e. mutual inductance and capacitance allow us to use simple circuit analysis and ignore the actual fields). This obviously is useful because of the simplicity in modeling systems.

In filter theory the abstraction is taken further, where electromagnetic coupling of cavity resonators can be modeled as coupled RLC circuits, which is accurate for narrowband applications.

It seems intuitive to model conductive resonators as RLC circuits. And the abstraction can be taken further to dielectric resonators. So could I take a problem that would be typically be solved by something like FEM analysis (fields interacting in irregular media for example) and decompose it into a finite amount of coupled circuits? This would lead to a numerical solution of how energy is transferred by the fields, without using typical numerical methods such as FDTD, FEM or MoM. I believe something similar to this exists for transmission lines, but I'm still looking into that.

Does this already exist? Or is there an obvious reason why I could not model any problem as coupled resonators (ignoring for now the awkward problem of bandwidth limitations)? I think for many problems it would be more efficient to solve problems using a circuit model than a variational or finite difference approach. My search thus far hasn't found anything I'm thinking of, so I would love to hear the thoughts of some more experience engineers.

Specific electromagnetic problems can be modelled by relative simple lumped equivalent circuits. But this presumes that the essential electromagnetic problem has been solved before so that an equivalent circuit could be found.

Modelling a transmission by a RLC chain considerably reduces the problem from 3D EM to 1D, ignoring all possible wave modes besides TEM and also omits many relevant frequency dependent effects. In other words a huge simplification that may be appropriate for some applications but useless for others.

A full EM problem requires a solution of the Maxwell equations.