While the purity argument does make the method get(Object) suspect, the underlying intent is not moot.
There are various class and interface families that slightly redefine equals(Object). One need look no further than the collections interfaces. For example, an ArrayList and a LinkedList can be equal; their respective contents merely need to be the same and in the same order.
Consequently, there are very good reasons for finding the matching element in a set. Perhaps a clearer way of indicating intent is to have a method like
public interface Collection extends ... {
...
public E findMatch(Object o) throws UnsupportedOperationException;
...
}
Note that this API has value broader that within Set.
As to the question itself, I don't have any theory as to why such an operation was omitted. I will say that the minimal spanning set argument does not hold, because many operations defined in the collections APIs are motivated by convenience and efficiency.
