I like the proposed set.get() method, personally.
Sets have been implemented in many languages, but I've only seen one that implemented this functionality (the "arb" function in SETL). For the most part, it seems that this is an uncommon need.
Also consider that there is value to keeping the set-api as simple as possible. Right now, anyone who was exposed to the basics of sets in school can understand the set-api with a near zero learning curve. Some of that would be lost if you add methods that make identity/equality distinctions or that fetch the same arbitrary value over and over again.
Besides, it is trivial to write a short function that encapsulates this behavior if it is part of your personal style of expression.
The existing methods aren't great for accomplishing this, mainly because they're obfuscatory. "iter(s).next()" is probably clearest, and at least will throw a StopIteration exception if the set is empty. "for x in s: break" is just confusing ...
A short comment would do wonders.
P.S. It is weird that this thread is gaining traction at the same time as the moratorium thread. Go figure :-)