I don't see how we can possibly break out of this cycle without revisiting the notion of an infinite-growth economy. Until we curb human population and energy consumption, we'll continue sprinting from dead-end to dead-end.
And we have, for all current intents and purposes, an infinite supply of nuclear, solar, and wind energy.
Further, I question the notion that solar and wind power are infinite in supply. At some point, absorbing solar radiation that would otherwise heat the surface of the earth must have some effect on global weather patterns, and a similar argument can be made for wind power. I don't think we're anywhere near that point, but it just goes to show that the "infinite growth" mindset is extremely problematic in the long run.
As for human population, this is true of first-world countries, but not universally true. India is an example of extreme demographic growth.
Any way you want to cut it, our power (or, more generally, resource) demands cannot grow infinitely. Where you are correct is in pointing out that the population constraint is fundamentally at odds with the geopolitical and economic need for demographic growth. This is precisely the point I'm lamenting.
The biggest issue with nuclear is that it, by itself, is entirely insufficient to deal with the problem. And the best policy solutions to climate change--namely, a refundable carbon tax--would themselves encourage the proliferation of nuclear to the extent nuclear is actually helpful.