Set-Tru style chucks are properly used by loosening the chuck mounting bolts just enough to allow the pusher screws that bear on the loose fitting buck plate, then using the pusher screws to true the part, then snug the mounting bolts again. Then the chuck will not move during the operation. Never a problem when done properly.
The amount the body of the chuck actually can move is limited to about 0.030, so unbalance due to the body being offset isn't usually a problem at normal operating speeds. Relative to the entire mass of the chuck, the offset weight is insignificant. If you were spinning at 10K on a 12" chuck, not that's another story. But it's no problem if the lathe is an industrial machine. I'm not so sure I'd want to do it on a benchtop lathe, but in reality, the speeds normally seen there won't pose any balance problems.
In theory, once you dial in a Set-Tru style chuck, you can chuck and unchuck with little or no lose of accuracy. Even when changing bar size. On a brand new chuck, this is probably a reasonable expectation. But like all scroll chucks, the jaws and scroll wears, and even if you dial in the chuck on one diameter, it may not run true at all other diameters. It's not realistic to expect it from a worn chuck. That's not really the intent, anyway.
Frank brings up a couple of good points. If you are making a part from raw stock, and will be parting it off complete, there is no reason to try to make the rough bar run dead true. Just make the part and cut it off. Nearly any average 3 jaw will be accurate enough for that, even if you start with a finish sized bar, unless you have specific requirements for concentricity. I think people probably worry too much about making things absolutely concentric to their starting stock diameter. After years and years of making parts per drawing for all sorts of industries, rarely is a part designed so that features required to run together that aren't able to be machined together. At times, one end, or an ID is required to be concentric within certain limits with other features. Then things need particular attention, but by and large, any decent 3 jaw can go merrily about its business of holding work and still stay within drawing limits. That's not to say that I've never seen requirements that certain features run very closely together either, but that's the exception rather than the rule.
Often when that is the case, Frank's other point comes into play quite handily. Soft-jaws. Any 3 jaw with two piece top jaws should be set up with soft jaws made of either aluminum or low carbon steel that can be bored or turned to closely fit the finish machined surface from the previous operation. Many parts can be machined from bar stock at one chucking, then parted off, flipped around and chucked in bored soft-jaws and hold TIR within 0.001 easily. They also can incorporate a stop for establishing OAL held closely at the same time as the second (or third, etc.) operation. The uses are many.
Bottom line, to me, is that if you have a decent 3 jaw, and some soft-jaws, you may not really need to spend the money on an adjustable 3 jaw. They can be nice, but they're hardly a necessity. By decent, I mean a chuck that will grab most anything you put in it within 0.001/0.002. Mine do, and I don't ever feel like I should be doing better. When I need to have good TIR, there are ways to get there without much bother.
