Well I move them myself growing or not. I often when rooting cuttings I have to up-pot them, so if they can handle it then, they certainly can handle it when bigger and older and more adjusted.
I have had live plants sent to me in the mail, I had no choice but to put it in a pot. One I just got is green house grown so it needs to be acclimated to full sun besides being ripped out of soil, mailed, which took 3 days and potted in different soil, no greenhouse, cold temps too, it's 40 right now outside. It looks fine. They are tough plants if you ask me. Often I hear they like tight roots, although I also hear in ground out produce in pot figs. My guess is because of the small pot size, it can't really grow and be more productive. Mine are all overpotted slightly when I transplant. I go from a 5 inch pot to 3-5 gallons, then to 15 gallons. I'm from the school of giving a plant room to grow. Also I use fabric 15 gallon pots, and because they air prune in these, it's like a 30 gallon hard pot. I may up figs to 20 gallons, maybe some favorites to 30 gallons, but no more. I will root prune at that point every 4 years, or until the fabric pot gives out. Everybody has their own methods. i never lost a tree yet doing this.