But for the most part the issue with pricing is about making the grid viable for renewables and running natural gas plants as to stabilize the grid. That would have been necessary either way.

Nuclear could actually help to alleviate the integration costs of renewables, though. For starters, you need less gas backup if your baseload (or at least some part of it) is covered by nuclear, and also less adaptations to the existing grid, because hey, it was designed, among others, for nuclear power plants.

It would be especially helpful in winter, because to get to a high share of renewables in winter (assuming we also use a high share of heat pumps) we will need long term storage from other seasons (or import hydrogen/ammonia), and I really doubt those options will become cheaper than nuclear, existing or even new, anytime soon. Green hydrogen is very expensive, and likely always will be in Central Europe, because transporting that stuff here from better suited locations is also expensive. So the less we need, the better.

Funnily enough, nuclear power plants could also provide district heating in addition to electricity, which I reckon would be massively helpful for the heating sector and getting through winter (and make the plants even more economical). The German Konvoi reactor (the design of the newest three plants we just shut down) is even designed to do that, but it was never put to use here (except in Greifswald, but that was an evil Soviet design Germany shut down in 1990).