Grid-scale storage doesn't necessarily mean lithium batteries. It could mean redox flow batteries, it could mean pumped hydro, it could mean gravitational potential storage, it could mean pressurised air in abandoned mineshafts. It could even mean smart grids with dispatched domestic batteries and dispatched EVs reverse charging back to the grid.
Nuclear is a great energy source, but it's not renewable. If we start rolling out nuclear all over the world on a large scale, we would sooner or later run out of nuclear material. I've heard estimates as high as 200 years, and as low as 50 years. The long-term future has to be something renewable, and all the renewable energy sources we currently know of are intermittent. Therefore there needs to be some sort of storage to smooth out the short term discrepancy between generation and consumption.
I do believe nuclear has a role to play. It could have seriously helped us as a stepping stone to get us from fossil fuel-based generation to renewables. It's my personal opinion that it's a bit late for that, and wind and especially solar are very competitive now, from an economic perspective. Having said that, I still see value for nuclear in the future, I just think the bulk of our efforts should be elsewhere.
FYI I worked in the energy sector for over a decade, in market modelling, simulation, optimisation, and control theory, and I helped drive policy and governance, especially as it relates renewable generation.
There are very different constraints on something portable, like a phone, laptop, car, or even plane, compared with something like an electricity grid.
You need to have high energy density for cars, planes, and phones. You don't need high energy density for a grid. What's more important there is scalability and reliability.