However, we also risk an extinction event if we don't get carbon emissions under control, so turning a known 100 year risk into a several thousand years possible risk feels like a good bet.
I don't know of anyone suggesting that climate change is going to be an extinction event. Changing patterns of human settlement, and the state of human civilization? Certainly. Extinction? Doesn't seem likely right now, from everything I've read.
It's certainly going to be, and is already, an extinction event for many other species. While it's true that humans probably won't go extinct as easily, billions of lives may be lost to collapsing ecosystems. We can't feed ourselves at large scale without an ecosystem to support us. At this point, that risk is looking much, much worse than the risk carried by nuclear waste in the long term.
That's an awfully cynical way of saying that billions of people will be displaced and die because of lack of food, floods, that migratory crises might lead to actual live weapons getting used for first countries to "defend themselves".
But sure, it's not an extinction event. Just billions of deaths over the next century and an upheaval of our society. No biggie.
I'm not trying to downplay the scale and scope of climate change. I just prefer to use accurate terminology. If it was going to or was likely going to lead to the extinction of humanity, I'd want people to say that. Instead, it seems likely to lead to billions of people dying and billions more being displaced and a total reorganization of most nation states/cultures worldwide, along with (as noted above) significant extinction for many other species.
I lived through the fear (and shared it) in the 1970s about a variety of world- and civilization-changing transformations, and while I believe that the talk of them then was largely well-intentioned, the sloppy language that was used then turned into linguistic weaponry to be used against those arguing for the much-more-likely-to-be-true climate change that we are now facing.