The fundamental issue with computational climate models is an epistemological one. Fitting multiple models, and computational ones of high Kolmogorov complexity at that, to a single run of a unique instance is not science, never was and never will be. The very paradigm of climate modelling, as it is practiced in the last several decades is flawed, and should be abandoned immediately.
The proper approach is to seek a simple theory, that fits many experimental runs of multiple physical instances, but GCMs are as far away from this requirement, as anything ever can get.
Therefore it should be realized, there is no such thing as “climate science” as an autonomous field, independent of the general and as yet unresolved problems of physics.
Non-equilibrium thermodynamics of complex systems (with a vast number of non-linearly coupled degrees of freedom) in the presence of significant radiant heat is one of the few areas of semi-classical physics, where little progress is seen, basically because of difficulties around proper lab models of such systems. That is, we still do not understand on a general level what’s going on.
But terrestrial climate is just one example of such systems. Why would anyone at her right mind expect to understand it better than the general case?