You are correct that much of these dynamics aren't captured in long-time-scale climate models, though. But it's being modeled quite frequently in different contexts, especially ecological ones.
Is it even remotely possible to accurately extrapolate to what the end points all may look like? It's highly likely it's not unless you're monitoring "everything" for 100s or 1000s of years to see just how far cycles will propagate.
But see the "temperature size rule".
There's too much uncertainty in most aspects of a climate forecast that far out for it to be a meaningful exercise. The same way long term climate average is a more accurate forecasts than attempting to use a weather model two weeks out.
In reality there are a number of practical constraints that place limits on the search space for these kinds of models, including ones that are likely genuinely decoupled from CO2 concentrations (think of things like mutation rates).