The other workaround I had heard for this is to have a non-Jew hired specifically to stand in the elevator and push buttons on behalf of Jews on the sabbath. But they'd still have to speak the floor so the attendant would know what button to push, right?

If so, what if an elevator had basic voice recognition? Speaking the floor number to a machine is no more work than speaking it to an attendant, right?

Maybe this rule interpretation was originally made back when elevators generally had attendants and did require some expertise to operate (e.g. to stop at the right spots)? And then didn't get rolled back when it became essentially trivial?