The memes of the climate

In a sufficiently large grid you will always have wind and in a global grid you'd also reliably have solar as base load.

Yes, except even with an interconnected European grid we're still not there. While I can't speak for how much landmass needs to be covered, we need to expand the capacity of the grid quite a bit. I'm not sure where the bottleneck in Germany is now, but a few years ago Danish wind power couldn't be exported much further than Hamburg. Since then the Bundesnetzagentur seems to have been handing out expansion permits left and right, but a grid expansion just across the EU sounds like a fever dream.

Furthermore the base load can be reduced significantly with smart sheduling of energy usage.

Sure, and we're being "motivated" by paying a larger transmission fee during the evening peak in Denmark. But still I haven't heard of people doing much more than not running their dryer during peak or maybe scheduling their EV's charging later. For smart grids to actually work we need distributed energy storage. People still need heating during peak. And as I've stated elsewhere in this thread, storage is expensive. What I wrote about was almost going off-grid, which is insanely expensive, but storage will still be too expensive for most and impractical for many. So most people will just pay the increased price for the power, and not make the huge investment in storage.

Finally nuclear is no gurantee of baseload coverage. Nuclear power plants require a lot of water for cooling, like all thermal power plants do. With climate change the reliability of rivers providing enough water and the water being cool enough to not cause an ecological desaster downstream is becoming less and less reliable.

Firstly, that depends on the implementation. You mention rivers, and your instance is a ".de", which explains your argument. But in a country like Denmark we have enough coast to build nuclear power there. Which was what was proposed back the 70s and early 80s.

Secondly, the time when we require the most power generated by power plants is during winter. As you yourself pointed out, the shutdowns occurred during the summer.