And warming, while accurate, doesn't really define what the real problem is. Warming isn't the problem. It's what happens as a result of the warming that's problem. The additional energy into the climate system shifts the climate, which we, as a civilization, depend on. Also, warming gives the impression that every place on Earth is going to get warmer, which is not the case.
In other words, because the innumerate can't quite grasp what "global warming" and its implications mean, we're going to use a far less accurate term for propaganda purposes. "Global warming" as a label does not given the impression you claim it gives. I think a huge part of the problem is this ridiculous doublethink and cognitive dissonance.
Especially the cognitive dissonance that goes into claiming as you do that we have very accurate models of how the Earth's climate is changing - via global warming - yet still claim that we're ignorant enough of the situation that we have to use an all-encompassing label "climate change" that means by definition any sort of climate change possible.
Since then, the science has only improved. We've gone from basic physics models to complex integrated global climate models. And they all show the same thing.
Namely, that we've still haven't been able to improve a bit on the original estimates of Arrhenius about the temperature forcing effect of a doubling of atmospheric carbon dioxide. Despite a century of work on the most important parameter of so-called "climate change" now has the same error estimate as Arrhenius's original estimate.