You bring up a good point on modeling and what we know.We can’t make models accurate enough to predict temperatures...
We know that CO2 correlates with temperature. We know that we are dumping a absolutely huge pulse of CO2 into the atmosphere. We know that atmosphere is a complex nonlinear dynamic system with "fat tails" uncertainty distribution on how it will react to this pulse. Could be relatively proportional, but also could be catastrophic with an unacceptable probability.
And we lack the models to actually say with any certainty that a catastrophic, civilization-ending outcome isn't in the offing.
It's the lack of models that compels us to control CO2. We know we are going to cause something to happen, but we are flying blind otherwise.