But you can't replace the gas peaker with 3% or 10% nuclear because in essence that gas peaker is supplying 100% of the power 3% to 10% of the time.
So you'd have to build nuclear plants that can supply 100% of the power. But once you have that you might as well use nuclear power 100% of the time because the rest is irrelevant. But that's about as far from cost-optimal as you can get.
As you mentioned, using batteries for seasonal storage is madness. So to get to 100% carbon free you have at least 2 other options:
1. use a different form of seasonal storage. China is experimenting with this. In 2026 they will double the world's pumped hydro storage capacity. But doubling isn't a lot -- the world doesn't have much pumped hydro. But it does mean they might start doing it at China scale in a few years.
2. Overbuild to avoid the need for seasonal storage. Solar works on cloudy days and in the winter. It just doesn't work very well. So you need a lot of it. Which is expensive, but still a heck of a lot cheaper than batteries for seasonal storage.
In reality, most places will probably say that 95% or 99% carbon reduction is good enough and keep their backup natural gas generators around for the occasional dankelflaute.