Okay, so lets say you figure out a way to build a desktop-sized nuclear power plant that doesn't produce any radioactivity. And, to keep it simple, lets say there's no other unusual, unexpected properties to do with safety.

We'll use it, and we'll use it a lot. It'll power the next generation of EVs, for example, and lithium batteries might be relegated to a few rare niche uses only. You wouldn't need to charge it, you'd just replace it every couple decades. If it's cheap it might find it's way into lesser appliances and devices as well. It's possible the biggest impact will come from things that wouldn't even work without that much energy density, and that we don't have a name for yet. If the devices are really cheap it might become a nuisance or environmental hazard, like wonder-material plastic has.

The one big issue it could have, is if there's a way for all that energy to release suddenly. You've explicitly ruled that out, though. (And for what it's worth, it's very, very hard to make real nuclear reactions finish both completely and quickly, to the point it just doesn't happen by accident. It's even hard to make happen on purpose)

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.

Don't know enough about the field but given how much of a threat and explosion risk fallout 4 cars are I would be very careful.

Nuclear energy involves radiation and shielding can be damaged or just leak over time. With how poorly people maintain their cars and homes, it's likely that they wouldn't maintain portable energy very well not to mention car accidents.

Plus it gives every person access to bombs of some level. It's hard to make portable energy that can't explode. Even modern batteries or gasoline explode, just on a smaller scale so the damage is limited. If it's an amount of energy that would power a car for years, that would be a lot more energy to release as a bomb. There's no way to 100% prevent someone from turning any amount of energy into a bomb. Only ways to limit the impact. We have technology to make cars run on a more energy dense version of gasoline, but it would be potentially more volatile. Every major car accident where a vehicle exploded, could have created a fireball that took out the houses along the road as well as all of the vehicles involved. It's all about scale.

And that's ignoring the financial and political interests. The oil industry has kept battery technology from improving for decades by buying it up and shelving it. It took ages for modern lithium ion battery tech to reach its current state, but it's based on technology originally developed in the 70s and bought up by Exxon who showed it off and then only slowly developed it and only used it for very specialized purposes. In late-stage, post-consolidation capitalism, any basic technology that threatens an industry is bought, patented, sat on, updated a little when the patent is up, repatented and sat on, etc. And lots of money funneled to politicians to over regulate it. So, it takes generations to move technology forward if an existing industry feels threatened. Happened with cars threatening horses and buggies, now it's batteries threatening oil. It requires a very rich person who doesn't bow down to the legacy industry in order to break that cycle. Ford did it with cars and oil, it looked like Musk was with electric cars and trains, but he gave in to the legacies for power in the end. Ford got power through his fascism alone and used it to further his business goals. Musk seems to have given up on business and is concentrating on information war for fascism instead.

There were plans for a train. Problem is, other then the obvious, that you still need a lot of water for the steam turbine.

I think there's a youtube video about it.

Realistically, we would probably use it. Should we? Well, first of, the idea that there would be 0 risk is just unrealistic. Everything carries a certain risk, no matter how small. So the question is: how big is the risk, and what are the potential consequences. Problem is with nuclear, even if the risk is small, the potential consequences if something does go wrong is the problem here.

But OK, let's say we managed to somehow magically get the risk to 0. Still no. It's a finite resource. It would just simply kick the can down the road. Only so much nuclear fuel will be available. We will probably start fighting wars over it again. Enough is enough. We're on a trajectory that, while it's still much slower than it should be, can bring us to a future where the vast majority of the energy we consume is renewable. Let's not fuck it up. Let's properly cure our addiction instead of using meth to get rid of our heroin addiction.

Because that's an impossibly big "if". Let's say you have a working reactor compact enough to fit in a car's engine bay. How do you protect it against car accidents? Theft? Fire? If you just pack on more and more shielding, either the car has to get bigger and heavier, or the reactor has to get even smaller.

Right now, a "micro-reactor" is the size of a shipping container. So while you could put it on a truck and power the truck to make it self-sufficient, you are at net zero, i.e. you're not moving any cargo. It's certainly not a personal vehicle.

While you could make a road train with a bunch of trailers (depending on how much power the reactor produces), which could make sense for places like the Australian outback, or crossing Russia or Canada, if the reactor gets T-boned on the road, you have a nuclear mess that's going to be extremely expensive to clean up.

Small reactors, like ones to power a neighborhood or a single factory are being developed and built right now. Some of these reactor designs cannot melt down and nuclear waste is solved problem, even with the absurd politics.