I still think you're oversimplifying it. Let's look at one common technology: cooling. Our current cooling solutions aren't carbon free. They use 6% of US electricity and are nowhere near carbon free. These aren't amounts that can be ignored either nor are they the only emitting technology we don't have a great solution for (heating you can pump hot water to homes, which nuclear provides a great solution to generate said heated water). It's worse because the feedback loop.

You also can't talk about next-generation reactors because they don't exist right now (at least in production).

What I'm trying to say here is that this doesn't help our pro-nuclear case. It is cherry picking post hoc analysis. Climate change would still be a real problem, even with our leg up. Because frankly, climate change is much harder than getting solar, wind, and nuclear everywhere. It is also bigger than America, the EU, and China (total of 54%).