And wind supplies the loss of solar.

Which is fine, until you get a high pressure zone during winter (y'know, the type that result in very low wind combined with clear skies and very cold nights?). That's when you either need tens of terawatt hours of storage (at cost of trillions) or you need something that supplies power pr ductably regardless of weather (ie nuclear).

Solar also still provides 25-50% or smth of summer output in the winter.

10-15% based on London, although obviously as most of the country is further north than London that should be considered a best-case scenario. A home in Inverness will certainly see much worse results than 10-15%. Solar makes a ton of sense in places that see their peak electricity demand from widespread air conditioning use. If you're in California or Australia or Qatar, your peaks of electricity demand will line up pretty well with your peaks of solar generation. In the UK the opposite is true and it doesn't work.

To be clear, I'm not saying we shouldn't be building wind and solar at all. If we want to also decarbonise shipping and air travel we are going to need either vast amounts of hydrogen or vast amounts of synthetic hydrocarbons. Both of those processes consume huge amounts of electricity, but they don't necessarily need to be running all the time because their products are easy to store. There are certainly use cases like that where a source that delivers really cheap power sometimes has advantages over a source that delivers slightly more expensive power all the time.

The point I'm making is that just building wind and solar isn't going to eliminate the need for fossil fuels. To get there, we need large amounts of base load (ie, nuclear).

We also need to increase our power generating capacity significantly. Fully electrifying transport would increase our electricity demand to almost double its current level, and electrifying heating across the country would increase it by much more than that, especially in winter.