The pessimistic outcome of climate change isn't "wild exponential predictions", though. There are well-understood mechanisms, the margin for temperature increase beyond which modern society collapses is pretty thin, the exponent comes primarily[0] from our economy which has an assumption of exponential growth built-in and will collapse if it suddenly turns into s-curve, and we also have a model of a runaway warming feedback loop as our neighbor in the Solar System.
Also worth remembering is that climate change isn't really about climate. It's about our society. Earth doesn't care about temperature, and life on Earth will happily survive whatever we can possibly throw at it this century. All that matters is that climate change puts pressure on societies around the world, and with enough pressure our entire civilization will collapse, and you and me and everyone else we know will die a horrible death.
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[0] - There are also environmental feedback loops ready to take over the growth of average temperature that have gained attention recently.
Hundreds of millions of people migrating from areas that become uninhabitable from sea level rise and increased temperatures, trying to get into any country that's less affected. Europe just almost tore itself apart over few million war refugees, imagine 100 times more people, with nothing to lose and a valid argument that it's all our fault they don't have a home now.
Food pressure, as arable land is lost to the sea and temperatures[0], plus collapsing ecosystems as insects and plants with high vulnerability to temperatures die off. Food prices increase, risk of food shortage increases too, and so does social unrest.
As some land is lost, other land becomes available, "defrosted" by the changing climate. With reduced agricultural capability and migratory pressures, nations will want to compete for both that new land and resources available on it. This could lead to war.
I could elaborate, but let me instead tell you to look at the problem in reverse: think of how little it takes to cause "mass horrible deaths". Most people live in cities now, and most cities are fed "just-in-time", which means there's 3-5 days worth of food in them. Imagine what happens if you break that supply chain for more than a week. Imagine this happening to multiple cities in a country simultaneously.
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[0] - You can't e.g. think that a +4°C Poland can just switch from wheat to bananas. Bananas may like the new summers, but won't survive the winters.
> For example, at the end of the last ice age, when the Northeast United States was covered by more than 3,000 feet of ice, average temperatures were only 5 to 9 degrees [Fahrenheit] cooler than today.
If 4 degrees Celsius of global cooling (relative to the current climate) can cause large parts of the US to be covered by 3,000 feet of ice, then it's not unreasonable to think that 4 degrees Celsius of global warming could have an equally destructive effect on agriculture and society.
Also worth remembering is that climate change isn't really about climate. It's about our society. Earth doesn't care about temperature, and life on Earth will happily survive whatever we can possibly throw at it this century. All that matters is that climate change puts pressure on societies around the world, and with enough pressure our entire civilization will collapse, and you and me and everyone else we know will die a horrible death.
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[0] - There are also environmental feedback loops ready to take over the growth of average temperature that have gained attention recently.