The biggest problem with climate models is not knowing what people will do tomorrow. There is a terrible lack of working crystal balls, unfortunately.
And climate models are incredibly conservative. In the face of near complete ignorance on an issue, a constant based on the current situation is input as an approximation or else a simple linear function of time is used (solar insolation is a fixed constant or else only slightly allowed to change because there aren't any non-linear models to predict anything different for the sun.) In the face of partial knowledge, such as with clouds where our detailed measurements of winds aloft and geographical impacts on it and other measurements are sorely lacking or our available compute power simply isn't up to the task, approximations are used (and updated regularly) that are based upon actual observations and extrapolations from there. Where good physics is known and the compute power is available, such as with line by line radiation physics, then fairly accurate modeling is used. But scientists don't go around making stuff up and putting it into the models. So if there is no knowledge on the non-linear responses of the Greenland ice sheet, a simple linear model is used despite the fact that it's known that the linear model doesn't work right. Without a good baseline to justify some non-linear model, it's avoided.
The sad thing about that is that non-linear equations have to be treated with rather different mathematical analysis than is used in models today. Such physical system states are governed by a potential, V(x;c), that can be described (at least in part) by a point x, which is an element of the field Rⁿ, that minimizes the potential. Changing external conditions change the values of the control parameters c; changing c, in turn, changes the shape of the potential V(x;c). As the shape of the potential changes, the original global minimum in which the system state sits may become a metastable local minimum (because some faraway minimum assumes a lower value), or it may even disappear. Such a system state may also quite literally jump from one local minimum to another. Deciding when and to which minimum the jump occurs is (at least in part, again) the subject of two commonly applied conventions, the Delay Convention and the Maxwell Convention. The essence here is that the dynamical considerations can be brought into elementary, static catastrophe theory by bringing back in the time derivatives of a system. In short, non-linear equations combine into moving cusps and sudden folds and must be analyzed as a dynamic catastrophe system of equations. But this just isn't handled in climate modeling. Yet it's still true that system collapses and sudden shifts CERTAINLY DO happen in reality. But no climate model I've heard of captures any of these sudden transitions.
There is a great deal that remains yet to be discovered. And the specific nature of the interface between the Greenland land mass underneath the ice sheet there and what exactly this interface is doing just isn't known well, for example, though we do know that it's responses are probably going to be non-linear in nature. But absent awareness of what we don't know, and absent details about aspects we only vaguely apprehend today, no one is going to just poke code into climate models for it. The unknowns still happen in reality. The only vaguely understood aspects also still happen in reality. But climate modelers cannot yet incorporate any of that until more is understood.
So they remain very, very conservative in the face of such RAPID change as is taking place now. They will always be behind the power curve. And this is especially bad in the case of systems with phase changes and other non-linear ways of combining under rapid change. Which is why LOTS more research is needed, and on a par with the speed with which we are changing things -- which means sooner than later.
Having _some_ experiences with this kind of theory (read Gilmore's 1981 edition of Catastrophe Theory for Scientists and Engineers), I have a much more profound respect for what _could_ take place that isn't captured in current models and probably never will be.
But an equally big issue, if not the most important issue, will be the lack of that working crystal ball about human behavior in the future.
The models help us discuss some reasoned minimum bounds and to ascribe the current very rapid warming to human impacts (because without those human impacts added to the models, you simply can't get "here" from "there.") I think it's the wrong question to ask "if the models actually worked" though. They don't predict the future and never will and aren't even supposed to. So the question can't be answered at all and is pointless to ask, my opinion.