Technically, in an airliner, that traffic would extremely likely show up in the ADSB readout, so, I think it’s actually a worthwhile callout to bring the traffic to the attention of the pilots, as, the only time ATC would bother notifying the pilots was if the traffic was headed for possible conflict.
In most cases, traffic to the 6 o’clock would not be an issue, but, I’m thinking something like a Cessna 414 with a jet approaching from the rear.