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I both agree and disagree. You make a lot of good points, backed by science. Though there were a few shortcuts in there. Just a "for example", even if the electricity generated to charge an EV battery is from fossil fuels (e.g. coal), the emission standards for that generation are generally tighter than for gasoline (which not only has to burn, but also has to be refined which adds to it's footprint). So you -again, generally- end up with less emissions from that charge than from a tank of petrol.
It is easy for both sides to ignore -or overlook- all the inputs necessary for any given technology/mode. That is a valid point, and does not make EVs a panacea. I agree. Though they are at least better. Which can then get into necessary enhancements to the power grid to support EVs as they become more ubiquitous (not cheap).
I think the bigger point with climate change is that sudden changes lead to extinctions. Left to its own devices, our climate slowly changes over time. Yes, it's been hotter, and it's been colder. But most of the time that didn't happen within a century. When it did, the dinosaurs died out. The Permian Extinction happened. Heck, there is some evidence that a minor impact caused the Dark Ages, wherein lots of people died because crops failed, etc. Rapid changes in climate are bad. They allow little opportunity for adaptation.
That said, we do need to adapt because it's a reality now. The 1st World nations will have little difficulty with that. They won't like it, and it probably won't be cheap, but they can do it. The rest of humanity, not so much. You can care or not (up to you), but it is the reality we face, and their will be difficult choices in our future.