I agree storage is a problem.

But the concept of “base load” is outdated. As I mentioned in another comment - Because actually “base load” nuclear is terrible in a grid increasingly full of nearly-free variable sources (solar&wind). The nukes need to stay at 100% all the time selling their power at a high fixed price to have any remote chance of being economical. Cheap variables push nuke's expensive power off the grid during the day, and increasingly into the evenings with batteries. This is unavoidable in an open energy market, and is fatal to the economics of nuclear.

The only way you can make it work is state subsidies and/or forcing people to buy the more expensive nuke power. Which will be unpopular. But maybe you can sell it as a “grid backup fee” or something.

May be base-load is not the best term but in case if batteries and other storages will run out during long cloudy stretch with weak winds nuclear will at least allow to power critical infrastructure. It’s bad that some consumers will loose power but less bad than total apocalypses when the storage is empty and you have no unintermittent power source in the grid.

Storage is not just 'a problem', it doesn't exist and won't for many many decades.

The planned solution is hydrogen power plants, but no one wants to build them because the infrastructure, including electrolysers, is way too economically unfeasible.

Therefore, Germany is and will continue to be dependent on coal and gas, as these are the main producers every night. That's your 'grid backup fee' for you.