In order to replace the world's current energy mix with nuclear, we'd have to switch on a new nuclear plant every day for the next several decades. All of that new infrastructure would also require massive amounts of fossil fuels to build (which you've magically made illegal) and would only last a few decades before having to be replaced (presumably without requiring any fossil fuels by then).
There isn't even enough copper on earth to electrify everything.
U235 has an energy density around 80,000,000 megajoules per kilogram (MJ/kg).
Burning coal has an energy density around 24 MJ/kg for lignite (a lower grade of coal) to about 32 MJ/kg for anthracite (the highest grade of coal).
This makes utilizing U235 for energy around 2,500,000 more efficient than coal.
If we used thorium-232 instead, the theoretical energy density is around 79,000,000 megajoules per kilogram (MJ/kg) if considering the full lifecycle of the reaction.
The physics speaks for itself, regardless of people too dense to understand numbers.
Just because fossil fuels own our governments, industry, and most societal mechanisms, doesn't make the world they've fabricated real.
Usage of fossil fuels implies utilizing oil as a fuel. In other words, other usages of oil are still on the table -- plastics, chemistry, etc.
Infrastructure would not be so difficult to electrify. We already all know how to do it, and many countries are much further along than the US.
Water heating can be electrified. Heat pumps are already superior to other methods of heating / cooling. Trains can be electrified. Semis can be electrified.
I believe it would not be much of a challenge to make nuclear powered aircrafts with today's technology. It seems crazy because nuclear anything has been made to seem crazy, because it is literally free energy. The cost is overcoming our fears, and putting in some work to make it infallible on safety.
We have all the tools and all the capabilities. There are no longer excuses. The technology is here and has been here for a long time, to make a society that flourishes in every fashion.
There isn't even enough copper on earth to electrify everything.
Your scenario isn't a miracle; it's a pipe-dream.