He neglects to mention that nuclear energy isn't going to affect the transportation issue...
Not by itself, no.  But there are so many Li-ion battery technologies either already in production or just about to hit, plus supercapacitors, plus the Firefly revision of the venerable Planté cell, that this problem should not be regarded as a roadblock.  Sure, any one of these technologies could have something which prevents it from becoming cheap enough... but all of them?
At least Li is a fairly common element. What would be good as far as common-elements concerns, would be a "Sodium-ion" battery. Might be heavier, but may pack a decent punch like the Li-ion cousin. But that may be a wish, as Li is liable to get scarce or expensive, while Na is "dirt cheap".

Lithium is fairly expensive. A lot of the cost is processing raw material to get it. Making sodium and aluminium has the same problem. Electrolisis is a major cost.

How nukes can serve transportation is to have electrified mass transit. Buses and trains, both passenger and freight. No fun, but a commute is possible. Battery cars (any battery) may be rich peoples' toys in the long run. One good thing about extensive mass transit is that drunk driving will no longer exist.

One good thing about extensive mass transit is that drunk driving will no longer exist.
Don't be so sure; running buses and trains is a very boring job, and the personnel have been known to use substances to make their time more bearable.
OK, you got me. :) What I meant, of course, was that it would cease to be a major problem becuse commoners wouldn't be driving. With a vastly smaller pool of drivers, it would almost stop being a problem. In a virtually car-free future, drunk driving will be as rare as that other type of drunk bus driver, the drunk airline pilot. Laws could be zero tolerance. A bus, train, or aircraft operator gets caught, and they lose all vehicle operator priviledges forever. Attrition will reduce it nicely. Want to drink? Don't drive!