In fact I did cut both ends at the same time. However, I was not using a ball cutting tool. I was making a series of cuts using (in effect) x-y coordinates calculated as "turns" on the cross slide and compound rest (set at 90 degrees to the cross slide). You might say I was doing manual CNC. Here is where my technique was wrong: If the first cut is at .005x, .005y, and the second cut is at .010x,.010y then in theory, after the first cut one can just move another .005,.005. In practice, however, there is so much play in the system that what you actually have to do is restart at 0,0 before each cut (moving "in" to 0,0 to remove any backlash); this takes a lot more time. So - left half made using correct technique, right half made using wrong technique.
I did this more as an experiment than anything else. I would not use this method for turning balls unless I absolutely had to, but I thing it can be a useful method for making unusual profiles in the absence of a CNC.
P.S. to gus: Very nice work on the rotary table and steam engine.