Does a nuclear reactor not run day and night, wind or no wind, in the same way as any other 'traditional' power plant? yes it does. If you build a nuclear plant you know how much you'll get out. You don't with wind farms hence massive margins compared to what turbines are rated for.

With wind you are totally reliant on the weather, which is also why offshore wind tends to work better as apparently wind patterns are more constant and predictable.

Your three bullet points are all strawman arguments.