At the edges of a triangle, when it doesn't cover all four pixels in a quad the pixel shader is still evaluated on all four pixels to calculate derivatives and at the end the results for pixels outside the triangle are thrown away. Your pixel shader better not blow up outside the triangle or you'll get bad derivatives for the pixels that are inside the triangle.
As triangles get smaller, the percentage of pixel shader evaluations that are happening outside of triangles goes up. In the extreme case if the triangle covers only one pixel, the pixel shader is executed 4 times and 3 results are thrown out! This has started to become a problem for games with high geometric detail and it's one of the reasons why Epic started using software rasterization for their Nanite virtualized geometry system in Unreal 5.
You might say "why don't you just stop doing this approximate derivative thing so you don't have to execute pixels that are thrown away? Are derivatives that important?" The answer is that derivatives are used by the hardware during texture sampling to select the correct mip level, which is pretty much essential for performance and eliminating aliasing. So you'd have to replace that with manual calculation of derivatives by the application which would be a big change.