Depending upon your age and prior body injuries (yeah, if we had known we were going to live this long, we would have taken better care of our bodies, or at least not don't quite as many stupid things in our youth), standing or sitting for very long can cause pain and it's nice to change it up. I think it would be possible to sit and cast with my ladle, but I suspect that I would need to redesign the casting table to be lower or I would need the chair to be bar stool height.
From a purely safety standpoint, an argument could be made that standing is better since if you spill molten lead toward you, you are more likely to be able to jump out of the way than if you were seated and subject to it landing in your lap. I wear a leather welding apron when I'm casting, so I'm hoping that it will give me an extra second or so to push away from the table before I end up getting broiled.