The blur happens because the stars shift slightly from frame to frame as the Earth rotates. If you apply a median stack without first aligning the stars, the stack treats their changing positions as differences and smears or softens them.

To avoid this, align the images on the stars before stacking. A dedicated alignment tool for astrophotography, such as align_image_stack, can register the frames so the stars line up, and then the stack can reduce noise while keeping the stars sharper.

In short: median stacking can work for noise reduction, but only after star alignment. If the frames are stacked unaligned, star motion will cause blur.