In terms of home power, nuclear power is insanely cheap. Specifically Thorium power. There is not much reason we could not power cars with miniature nuclear generators if we put enough research into it so that crashing into them doesn't leak radiation everywhere, but right now that is not feasible, so mobile power would still be an issue.
The biggest reason it isn't used internationally is mainly because every government is scared of a meltdown even though any modern Nuclear engineer would build a reactor which has a non reactive default state, that even if catastrophic failure happens it can not melt down.
Very few of those reactor designs have ever been put in practice (I don't know of any that have) because of the perpetual banning of new reactors in many parts of the world.
The other reason is the massive up front costs, mainly because we have had this international armistice against it for two decades, nobody has the manfacturing tech to make these reactors in a rigorous patterned way.
So it is a perpetual failure, but if we had sustainable nuclear power with the modern safe reactors, specifically Thorium power, energy costs would probably drop in the long run because a single reactor can last a hundred years and the fuel costs nothing compared to the costs of maintaining the plant or building it in the first place or staffing it properly. But modern designs would not require as much oversight if their failure state is to power down.