why is it always assumed that the suns output cant vary much?
Because science isn’t always science, sometimes its just another religion with rigid dogma.
During the Cretaceous Period 145 to 66 million years ago polar regions were free of continental ice sheets, their land instead covered by forest. Dinosaurs roamed Antarctica, even with its long winter night. I have yet to read a reasonable explanation for this phenomenon. I personally think the sun was putting out more energy during that era.