Energy density almost doesn't matter for grid scale things. It's not like we don't have space where we could put batteries. Cost is really the only important measure and nuclear is very expensive, while batteries keep getting cheaper.
Energy density matters greatly because cost is a function of the material you have to handle and the amount of facilities you need to build to generate the power in the first place.
In that case energy density would be reflected in the cost. That is why cost is often used to compare energy technologies, and not cherry picking a random metric which favors one particular technology.
The cost of nuclear reflects the fact that toxic waste you can't see, smell or taste is scarier in the minds of the public so we insist upon far more government involvement and rigor in the construction of nuclear plants and insist they pay their decommissioning costs up front. Dare I say nuclear's costs are internalized whereas other modern manufacturing's costs are externalized.
They don't need a whole nuclear power station built around them though.
They also have orders of magnitude (10^3 - 10^4) more charge/discharge cycles than uranium.
This is a joke, right?
Its an observation that comparing vastly different technologies using just a single metric produces mostly misleading asinine statements that aren't sufficient to influence any meaningful policy or engineering decisions without additional supporting explanation and justification.