Eryngiums certainly don't like root disturbance but the method of propagation that is use doesn't stress the plant ( the potted plants are mounted on mounds of sand and left to mature before root cutting are taken from outside the pot, in the sand mounds, which are easy to move).
They produce very long tap roots, like carrots and parsnips, so a deep pot is advisable and they like sharp drainage so put plenty of grit in with your compost. They will happily establish in a pot before you have to worry about planting, although they dont do well if left potted for an eternity.
I moved a Eryngium a few years back which was sickly in the wrong place and it recovered well and is now a monster in the right place, but I wouldn't recommend doing this out of habit. They don't really like it because all their root is in one basket so to speak and yes, they need support topside to reward you with the finest displays.