I've got a high quality and fairly expensive one piece BR rest that holds my BR gun perfectly still(no not the gun in the photo), and that's about as good as it will ever get, but a nice stoutly built bipod and the aforementioned pump bag is nearly as good when using my non benchrest rifles.
The trick is that the way the rifle is held, and the least offending torque imposed on it, or I should say at least imposed consistently, is what allows for the most precision. For example if you are using a squeeze bag, and it settles more and more each shot, and you are moving it around to reposition it back to POA, and the bottom of the rear of the rifle sits differently each shot, etc, etc, then some precision is lost in that process. It might not be much lost on a decent sized target but it probably won't win you a Benchrest match either.
That's not including other things affecting precision capability.
I was struggling with my tactical bags down prone, and off benches, and using pads to raise or lower them to the most optimal height(for group testing), but that's a pain, thus why I looked and found a better solution.
Of course for dynamic shooting you'll just have to use the various tactical bags the best you can to secure the most solid positioning.
I'd rather use my tripod much for that kind of stuff anyway since I don't shoot precision style matches like NRL22 anymore.
Speaking of that I gotta show off my new Skout EVO pcp air rifle on said Fat Boy tripod. I have a wind indicator hanging off the antenna about 4" up from the scopes objective.