I for one predict that the new operator will appear very sparingly, in while loops and code golf competitions.
There are already so many complicated semantics about mutability, iteration, bytes/strings, scoping, et al. And yet somehow a tiny piece of syntax that finally lets us stop writing "while true/break" is the big pain point?
I'd expect the new operator to become the idiomatic way to write certain quite common things, for example regexp group matching and objects returned by dictionary .get() - currently you always need a dummy variable to check if it's not None before you use it.