> Second, it's not zero carbon if you include building the plants, since the plants have a limited lifespan, so there's still a carbon footprint for the materials.

Nothing is zero carbon either. Batteries have a very long supply chain that involves a lot of carbon heavy steps, and their disposal also creates pollution. The same goes for solar panels, but people conveniently choose to ignore that.

> we would run out of all easy to mine uranium in a few decades

We dont need uranium to run on nuclear power. There are several alternatives already.