Hi,
A possible solution to this issue could be to adjust the settings of the hillshade tool, such as the azimuth and altitude angles, or changing the Z-factor to adjust the vertical exaggeration. It may also be helpful to check if the input USGS DEM file has any missing or incorrect data that could be causing the pixelation in certain areas. Additionally, using other data sources or sources with higher resolution may also produce better results.
Another thing I would examine is the coordinate system. Is your DEM in a geographic or projected coordinate system? Best practice is to reproject your raster from geographic to projected before running the GP tool on it.