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It would still depend on a non-renewable resource that needs to be mined, with all the environmental destruction that comes with it.
And it would still produce nuclear waste, which we still haven't found a way to dispose of.
And in a vehicle fire, that nuclear fuel would spread everywhere even if it doesn't explode.
Meanwhile, battery electric vehicles can be charged by renewable energy that never runs out.
After the batteries have reached the end of their lifespan for the car, they can still be used in large battery banks to buffer peaks and shortages in the electrical grid. And after that, they can be recycled almost completely.
We can reprocess used nuclear fuel. The term waste is a bit more nuanced than it's colloquial usage when it comes to the nuclear industry. A majority (90%+) is low level waste (used anti-c suits, gloves, paper towels used to clean up suspected spills in radiation areas). The actual volume of high level waste (fuel rods and core material) is very small. For context, the amount of spent nuclear fuel the United States has ever produced since the advent of nuclear power could be fit in a football field 11 meters deep.
In response to OP, no, putting nuclear reactors in cars or transport vehicles doesn't make sense from a practical standpoint, as smaller engines are less efficient than larger ones, controlling for design. And the safety aspect of letting any joe blow have easy access to highly radioactive material is not in everyone's best interest.
Reprocessing fuel is prohibitively expensive.
https://www.belfercenter.org/publication/economics-reprocessing-vs-direct-disposal-spent-nuclear-fuel
Cool, let's take some of the roughly $700 Billion spent on fossil fuel subsidies annually and apply it there instead of coal and natural gas plants.
I am more than okay with my tax dollars subsidizing reprocessing if it means significantly less nuclear waste sitting around.
One thing to point out is the energy density in nuclear fuel, even before reprocessing, is higher than all the energy that will pass through the same amount of lithium processed into rechargeable batteries, over the entire life cycle of that battery. A typical 1GW plant consumes an average of 70 kg of fuel per day, at a 90% capacity rate. So that's 24 hours x 90% x 1000000 kW, divided by 70 kg, for about 300,000 kWh per kg of fuel.
Meanwhile, LFP batteries are about 10% lithium and have 150 Wh per kg of battery weight. Let's say the battery can get through 10,000 charging cycles before recycling. That's 15,000 kWh per kg of lithium.
Obviously lithium can be recycled and uranium fuel can be reprocessed. We can also compare the very inefficient extraction of either element (uranium or lithium) from the actual natural ore pulled out of the ground. And the very involved manufacturing processes of turning that ore into useful fuel or batteries.
But either way, the overhead of mining physical stuff to support the supply chains of things that get used up, even reusable/recyclable durable goods, will always be there. Uranium genuinely is special in its energy density and requires closer examination of the calculations.