Easier to clean 90 degrees than a more natural angle. Same reason you see saxes at "horns down" held parallel to the ground.

Watch military bands in a parade. Horns down position for saxophones, per the reg, is to let it hang from the neck strap at a natural angle (45-ish) with right hand on the horn and left hand swings in time. But most Texas marching bands have saxes at a flat table-top carry with both hands on the horn.